Answer:
[tex]725\ degree=2\ revolution[/tex]
Explanation:
We know that 1 complete revolution is equal to 360 degrees. We need to find the number of complete revolution needed to draw the angle of 725 degrees.
Since, 1 revolution = 360 degrees
or
[tex]1\ revolution=2\pi \ radian[/tex]
[tex]1\ degree=\dfrac{1}{360}\ revolution[/tex]
[tex]725\ degree=\dfrac{725}{360}\ revolution[/tex]
[tex]725\ degree=2.01\ revolution[/tex]
or
[tex]725\ degree=2\ revolution[/tex]
So, to draw an angle of 725 degrees, there are 2 revolutions. Hence, this is the required solution.
How does the strength of an electromagnet depend on the current and the number of turns in the coil?
Strength of Electromagnet increases when either the "Current" or "Number of turns in a coil" increases.
They are directly proportional to strength of Electromagnet.
Explanation:
To compile, the power or intensity of a coils magnetic field depends on the following circumstances. The number of turns of wire within the coil. The amount of current running in the coil. An electromagnet is a temporary magnet; the magnetic field only survives when an electric current is running through it. The power of the electromagnet depends on how many coils you wind around and how great the voltage is.
SI is considered a consistent system because it
SI (International System of Units) is a consistent system in mathematics because it provides standard and consistent measurements based on fundamental constants of nature.
Explanation:In mathematics, SI (International System of Units) is considered a consistent system because it provides a standard and consistent way of measuring physical quantities such as length, mass, time, and temperature.
SI units are based on fundamental constants of nature and are internationally recognized and used. For example, the meter is defined as the distance traveled by light in a vacuum during a specific time interval.
Consistency in SI units allows for easy comparisons, calculations, and communication across different scientific disciplines and countries.
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how might building a new highway affect the cycles of matter?
Which type of radiation is used to make images of bones inside the body?
A basketball has a mass of 1 kg and is traveling 12 m / s . How fast would a 6 kg bowling ball have to travel to have the same momentum ?
a. 1 m/s
b. 2 m/s
c. 3 m/s
d. 4 m/s
Q1. After three half-lives of an isotope, 1 billion of the original isotope's atoms still remain in a certain amount of this element. How many atoms of the daughter product would you expect to be present?
Q2. By measuring the amounts of parent isotope and daughter product in the minerals contained in a rock, and by knowing the half-life of the parent isotope, a geologist can calculate the absolute age of the rock. A rock contains 125 g of a radioisotope with a half-life of 150 000 years and 875 g of its daughter product. How old is the rock according to the radiometric dating method?
what is the control center of the cell
True or fase
a force is always required to move an object from rest.
...?
A 17,000-kg airplane lands with a speed of 82 m/s on a stationary aircraft carrier deck that is 115 m long. find the work done by nonconservative forces in stopping the plane
The work done by nonconservative forces in stopping the 17,000-kilogram airplane landing at a speed of 82 m/s is 57,062,000 Joules. This is calculated by the change in kinetic energy of the airplane when it lands and comes to a stop.
Explanation:The question refers to the concept of work-energy theorem in Physics, especially involving non-conservative forces. The airplane is initially moving and finally comes to rest. Its initial kinetic energy (KE) gets transferred to work done by nonconservative forces, which in this scenario includes friction due to the aircraft carrier deck and air resistance.
The initial kinetic energy of the plane is calculated using the formula 1/2 * m * v^2 where 'm' is the mass of the plane and 'v' is its speed. So, the initial kinetic energy of the plane is 1/2 * 17,000 kg * (82 m/s)^2 = 57,062,000 Joules. When the plane comes to rest, its final kinetic energy is 0. As per the work-energy theorem, the work done by nonconservative forces is equal to the change in the kinetic energy. Therefore, the work done by nonconservative forces in stopping the plane = Initial KE - Final KE = 57,062,000 Joules - 0 = 57,062,000 Joules.
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The work done by nonconservative forces in stopping the airplane is [tex]{57,154,000 \, \text{J}}[/tex].
To find the work done by nonconservative forces (like friction and air resistance) in stopping the airplane, we can use the work-energy principle. The work done by the nonconservative forces is equal to the change in the kinetic energy of the airplane.
Step-by-Step Solution
1. Calculate the initial kinetic energy ([tex]KE_{\text{initial}}[/tex]):
[tex]KE_{\text{initial}} = \frac{1}{2} m v^2[/tex]
where:
- m is the mass of the airplane (17,000 kg),
- v is the initial speed (82 m/s).
[tex]KE_{\text{initial}} = \frac{1}{2} \times 17,000 \, \text{kg} \times (82 \, \text{m/s})^2 \\\\KE_{\text{initial}} = \frac{1}{2} \times 17,000 \times 6,724 \\\\KE_{\text{initial}} = 57,154,000 \, \text{J}[/tex]
2. Calculate the final kinetic energy ([tex]KE_{\text{final}}[/tex]):
Since the airplane comes to a stop, its final speed is 0 m/s.
[tex]KE_{\text{final}} = \frac{1}{2} m (0)^2 = 0 \, \text{J}[/tex]
3. Calculate the change in kinetic energy (ΔKE):
[tex]\Delta KE = KE_{\text{final}} - KE_{\text{initial}} \\\\\Delta KE = 0 \, \text{J} - 57,154,000 \, \text{J} \\\\\Delta KE = -57,154,000 \, \text{J}[/tex]
4. The work done by nonconservative forces (W):
The work done by nonconservative forces is equal to the negative of the change in kinetic energy (since they are doing work to stop the airplane).
[tex]W = -\Delta KE \\\\W = -(-57,154,000 \, \text{J}) \\\\W = 57,154,000 \, \text{J}[/tex]
Therefore, the work done by nonconservative forces in stopping the airplane is [tex]{57,154,000 \, \text{J}}[/tex] .
What is the sound intensity level if the intensity of the sound is doubled??
A potassium atom (atomic number 19) and a bromine atom (atomic number 35) can form a chemical bond through a transfer of one electron. The potassium ion that forms has 18 electrons. What best describes the bromide ion that forms?
A It is a negative ion that has one less valence electron than a neutral bromine atom.
B It is a positive ion that has one less valence electron than a neutral bromine atom.
C It is a negative ion that has one more valence electron than a neutral bromine atom.
D It is a positive ion that has one more valence electron than a neutral bromine atom.
Correct answer choice is :
C) It is a negative ion that has one more valence electron than a neutral bromine atom.
Explanation:
A bromide is a synthetic composite including a bromide ion or ligand. Potassium bromide (KBr) is a salt, usually selected as an anticonvulsant and a drug in the late 19th and early 20th centuries, with over the stand value increasing to 1975 in the US. Potassium bromide is applied as a veterinary drug, as an antiepileptic medicine for dogs.
C. It is a negative ion that has one more valence electron than a neutral bromine atom.
Explanation;Potassium atom and a bromine atom may form a chemical bond called ionic bond. Ionic bond is formed between a metal and a non-metal and involves the transfer of electrons from one atom to another,During the formation of an ionic bond the metal atom looses electrons to form a positively charged ion called a cation, and the non-metal gains electrons to form a negatively charged ion called ion. In this case, a neutral potassium atom with 19 electrons looses 1 electron to form a potassium cation with 18 electrons. On the other hand, a neutral bromine atom with 35 electrons gains 1 electron to form an anion (negatively charged ion) with 36 electrons.The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 780 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the verticl distance climed. Assume an average air density of 1.20kg/m^3 ...?
Final answer:
To determine the vertical distance climbed by the mountain hiker, we can use the relationship between air pressure and altitude. By applying the barometric formula and substituting the given values, we can solve for the change in altitude. The vertical distance climbed is 12.1 meters.
Explanation:
To determine the vertical distance climbed by the mountain hiker, we can use the relationship between air pressure and altitude. The change in air pressure, ΔP = P₁ - P₂, can be related to the change in altitude, Δh. Assuming the air density to be constant, we can use the barometric formula to find the change in altitude. The formula is given by ΔP = ρgh, where ρ is the air density, g is the acceleration due to gravity, and h is the change in altitude.
By substituting the given values into the formula, we can solve for Δh. We have ΔP = 930 mbars - 780 mbars = 150 mbars and ρ = 1.20 kg/m³. We know that g is approximately 9.8 m/s². Solving for Δh, we get Δh = ΔP / (ρg) = 150 mbars / (1.20 kg/m³ * 9.8 m/s²) = 12.1 m.
Therefore, the vertical distance climbed by the mountain hiker is 12.1 meters.
Final answer:
The vertical distance climbed by the hiker is approximately 1269 meters, calculated using the barometric pressure difference and average air density.
Explanation:
To determine the vertical distance climbed by the hiker, we can use the barometric pressure reading along with the average air density. The pressure difference (ΔP) can be used to calculate the height difference (h) using the barometric formula ΔP = ρgh, where ρ is the density of the air, g is the acceleration due to gravity (9.81 m/[tex]s^2[/tex]), and h is the height difference.
First, we convert the pressure difference from millibars to pascals (since 1 mbar = 100 pascals):
ΔP = (930 mbar - 780 mbar) × 100 Pa/mbar = 15000 Pa
Now, we can solve for h:
15000 Pa = (1.20 kg/[tex]m^3[/tex]) × (9.81 m/[tex]s^2[/tex]) × h
h = 15000 Pa / ((1.20 kg/[tex]m^3[/tex]) × (9.81 m/[tex]s^2[/tex]))
h ≈ 1269 meters
Therefore, the vertical distance climbed by the hiker is approximately 1269 meters.
A gas has an initial volume of 212 cm^3 at a temperature of 293 K and a pressure of 0.98 atm. What is the final pressure of the gas if the volume decreases to 196 cm^3 and the temperature of the gas increases to 308 K?
a. 0.86 atm
b. 0.95 atm
c. 1.0 atm
d. 1.1 atm
Answer:
For this we use general equation for gases. Our variables represent:
p- pressure
v-volume
t- temperature
P1V1/T1 = P2V2/T2
in this equation we know:
P1,V1 and T1, T2 and V2.
We have one equation and 1 unknown variable.
P2 = T2P1V1/T1V2 = 1.1atm
Explanation:
the guy above me is VERY correct
A 50 g mass hanger hangs motionless from a partially stretched spring. When a 65 gram mass is added to the hanger, the spring stretch increases by 10 cm. What is the spring constant of the spring (in N/m)? (Assume g = 9.79 m/s2. ...?
The spring constant can be calculated using Hooke's Law. By determining the force exerted by the added mass on the spring and dividing that by the distance the spring is stretched, the spring constant is found to be 6.37 N/m.
Explanation:This question is regarding the concept of Hooke's law in physics, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. Given that the spring stretches an additional 10 cm when a 65g mass is added, we calculate the force exerted by the mass on the spring as F = m*g = 0.065 kg * 9.79 m/s² = 0.637 N.
Then, using the equation from Hooke's Law, F = kx, where F is the force, k is the spring constant, and x is the distance the spring is stretched, we can calculate the spring constant as k = F / x = 0.637 N / 0.1 m = 6.37 N/m.
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A thin 2.09 m long copper rod in a uniform
magnetic field has a mass of 40.6 g. When
the rod carries a current of 0.229 A directed
perpendicular to the magnetic field, it floats
in the magnetic field.
The acceleration of gravity is 9.81 m/s²
.
What is the field strength of the magnetic
field?
Answer in units of T ...?
The strength of the magnetic field is approximately 8.22 T.
To solve for the magnetic field strength B, we use the equation that relates the force due to gravity to the magnetic force.
When the rod is floating, the gravitational force is balanced by the magnetic force. The gravitational force is given by [tex]\( F_g = m \cdot g \)[/tex], and the magnetic force is given by [tex]\( F_m = I \cdot L \cdot B \), where \( B \)[/tex] is the magnetic field strength.
Setting the gravitational force equal to the magnetic force, we have:
[tex]\[ m \cdot g = I \cdot L \cdot B \][/tex]
Now we can solve for B:
[tex]\[ B = \frac{m \cdot g}{I \cdot L} \][/tex]
Given the values:
[tex]- \( m = 40.6 \) \\g \( = 40.6 \times 10^{-3} \) kg (since 1 g \( = 10^{-3} \) kg),\\ - \( g = 9.81 \) m/s^2,\\ - \( I = 0.229 \) A\\ - \( L = 2.09 \) m,[/tex]
we can plug these into the equation:
[tex]\[ B = \frac{40.6 \times 10^{-3} \text{ kg} \cdot 9.81 \text{ m/s}^2}{0.229 \text{ A} \cdot 2.09 \text{ m}} \] \[ B = \frac{40.6 \times 10^{-3} \cdot 9.81}{0.229 \cdot 2.09} \] \[ B = \frac{0.4 \cdot 9.81}{0.47711} \] \[ B = \frac{3.924}{0.47711} \] \[ B \approx 8.22 \text{ T} \][/tex]
Setting the gravitational force equal to the magnetic force, we have:
[tex]\[ m \cdot g = I \cdot L \cdot B \][/tex]
Now we can solve for B:
[tex]\[ B = \frac{m \cdot g}{I \cdot L} \][/tex]
Given the values:
[tex]- \( m = 40.6 \) g \( = 40.6 \times 10^{-3} \) kg (since 1 g \( = 10^{-3} \) kg), - \( g = 9.81 \) m/s², - \( I = 0.229 \) A, - \( L = 2.09 \) m,[/tex]
we can plug these into the equation:
[tex]\[ B = \frac{40.6 \times 10^{-3} \text{ kg} \cdot 9.81 \text{ m/s}^2}{0.229 \text{ A} \cdot 2.09 \text{ m}} \] \[ B = \frac{40.6 \times 10^{-3} \cdot 9.81}{0.229 \cdot 2.09} \] \[ B = \frac{0.4 \cdot 9.81}{0.47711} \] \[ B = \frac{3.924}{0.47711} \] \[ B \approx 8.22 \text{ T} \][/tex]
Therefore, the strength of the magnetic field is approximately 8.22 T.
The splitting of a(n) ________ to produce energy is called a fission reaction. A. atom B. proton C. neutron D. molecule The splitting of an atom to produce energy is called a fission reaction.
Which of the following materials is likely to be the best conductor?
iron
sulfur
carbon
tin
Answer: Option (a) is the correct answer.
Explanation:
Metals are the substance which have excess of electrons. Therefore, they are good conductors of heat and electricity as they have mobile electrons.
Out of the given options, iron is a transition metal which are good conductors of heat and electricity.
Sulfur and carbon are non-metals, therefore, they are bad conductors of heat and electricity.
Tin is a poor metal so it will not conduct electricity effectively as compared to iron.
Thus, we can conclude that out of the given options, iron is likely to be the best conductor.
Geothermal energy is generated by the sun.
True
False ...?
A 12 g bullet is fired into a 9.0 kg wood block that is at rest on a wood table. The block, with the bullet embedded, slides 5.0 cm across the table. The coefficient of kinetic friction for wood sliding on wood is 0.20.
What was the speed of the bullet?
The initial speed of the bullet can be determined using the principles of conservation of momentum and the work-energy theorem. Conservation of momentum gives us the velocity of the block and bullet after collision, and the work-energy theorem using the friction force and the distance gives us the velocity.
Explanation:This question can be solved using the principles of conservation of momentum and the work-energy theorem. Using conservation of momentum before and after the collision, we can put: Momentum before = Momentum after. Therefore, (mass of bullet * velocity of bullet) = (total mass * velocity after). This gives us the velocity of the block and bullet together. From the work-energy theorem, work done = change in kinetic energy. Or, friction force * distance = 1/2 * mass * (velocity)^2. But friction force = mass * gravity * coefficient of friction, which gives us the equation 0.20 * 9.01 * 9.81 * 0.05 = 1/2 * 9.01 * (velocity)^2. Solving the equations together will give you the initial speed of the bullet.
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In 1831, Michael Faraday was the first to realize that an electric current could be induced by passing a magnet through a coil of copper wire. Which factor is MOST essential for the induction of the electric current?
Answer:
D
Explanation:
it is the correct answer on usa test prep
Two charged objects of +2Q and +1Q are placed a distance d from one another. The force between the objects in measured as 2F. If the charge on BOTH objects id doubled, what will the force between them be?
When the charge on both the given objects is doubled, Coulomb's Law indicates that the electrostatic force will become four times greater, resulting in a new force of 8F.
The original question asks about the effect on electrostatic force between two charged objects if both of their charges are doubled.
In the given situation, if we double the charge on both objects (from +2Q to +4Q and from +1Q to +2Q), then the product of the charges becomes 4 times greater because (4Q * 2Q) is 4 times (2Q * 1Q).
Therefore, if the force was initially measured as 2F, after doubling both charges, the force will become 4 times bigger, which is 8F.
This is represented by the option: c.
5 minerals used to make phones
viewed from earth two stars form an angle of 76.04 degrees. StarA is 23.30 light years from earth star Bis 34.76 light years from earth sketch a diagram modeling this situation and find how many light years the stars are from eachother ...?
Answer:
36.88 light years apart
Explanation:
use law of cosines to plug in A and B and use x as the C value you need to find with cosC = cos76.04
Which example provides the most complete description of an object's motion?
1. The ballerina rotated 10 times in 2 minutes.
2. Bobby threw a Frisbee 10 m through the hoop.
3. The turtle took 20 minutes to make it to the other side of the road.
4. The hiker followed a road heading north for 2 miles in 30 minutes.
Answer:
The hiker followed a road heading north for 2 miles in 30 minutes.
Explanation:
In order to describe the motion of an object, distance covered and time taken must be required. The total path covered by an object is called the distance travelled.
The hiker followed a road heading north for 2 miles in 30 minutes. This describes the motion of hiker. The motion shows how fast the hiker is moving.
Distance, d = 2 miles = 3218.6 m
times, t = 30 minutes = 1800 seconds
So, we can say that the hiker is moving with a speed of 1.78 m/s in north direction.
Hence, this is the required solution.
Answer:
In this case in option 4:
The hiker followed a northbound road for 2 miles in 30 minutes.
Explanation:
Hello ! Let's solve this!
To know the description of a movement we have to know the distance it travels and the time it takes to travel it.
In this case in option 4:
The hiker followed a northbound road for 2 miles in 30 minutes.
Distance: 2 miles
time: 30min
Then we can calculate the speed of the hiker
The internal kinetic energy of molecules produces ...?
What is the torque about the center of the sun due to the gravitational force of attraction of the sun on the planet?
Final answer:
The torque about the center of the Sun due to the Sun's gravitational force on a planet is effectively zero, as the force provides centripetal force for the planet's orbit, not rotational force.
Explanation:
The question asked relates to the field of Classical Mechanics within Physics, particularly regarding the calculation of torque due to gravitational forces. In classical mechanics, torque is the measure of the force that can cause an object to rotate about an axis. The torque (τ) can be calculated by the cross product of the radius vector (r) from the axis of rotation to the point of force application and the force vector (F), τ = r x F. However, in the context of a planet orbiting the Sun, the force of gravity provides centripetal force causing the planet to move in a circular path and does not contribute to the planet spinning or rotating about its own axis. Therefore, the torque about the center of the Sun due to the Sun's gravitational force on a planet is effectively zero.
A beam of protons is moving toward a target in a particle accelerator. This beam constitutes a current whose value is 0.50 μA. How many protons strike the target in 15 seconds?
if you break a bar magnet in half, each half
Answer:
If you break a bar magnet in half, each half becomes a magnet.
Explanation:
A substance which attracts or repels another similar substance is known as magnet. When domains align in single direction in a substance, it acts as a magnet. A magnet has two poles- North pole and South pole. Like poles repel each other and unlike poles attract each other. Mono-poles do not exist. So, when a magnet is broken into two halves, each half forms another magnet with two poles.
Answer:
If you break a bar magnet in half, each half will have a new south pole, a north pole and a neutral zone. In other words, two new magnets will be generated.
Explanation:
A magnet is a body of any material capable of producing a magnetic field and attracting itself or being attracted to another magnet or to any other body of iron, cobalt or other ferromagnetic metals (ferromagnetism is a physical phenomenon in which magnetic ordering occurs of all the magnetic moments of a sample, in the same direction and direction. In other words, the ferromagnetic interaction is the magnetic interaction that makes the magnetic moments tend to be arranged in the same direction and direction. This property makes the ferromagnetic materials they are intensely magnetized when they are placed in a magnetic field, and retain part of their magnetization when said field disappears.). Then the magnet is a material with natural or artificial ferromagnetic properties, which generate a continuous magnetic field.
Magnets are magnetically charged bodies, which generate a magnetic field around them oriented according to two poles: negative pole (also called South pole) and positive pole (also called North pole). Opposites attract each other (positive-negative) and equal poles repel each other (positive-positive or negative-negative). The line that joins both poles is called the magnetic axis. This line located in the central zone located between both poles has no attraction or repulsion capacity.
In the event that a magnet is broken into pieces, each new fragment will have a new south pole, a north pole and a neutral zone. That is, equal and opposite poles appear on each side of the breaking point. This happens even if the fragments are of different size.
___ acceleration occurs when an object speeds up
Explanation:
Acceleration is defined as the change in velocity over time.
When there is an increment or increase in the magnitude of velocity of a moving body then it is known as positive acceleration.
Whereas when there is a decrease in magnitude of velocity of a moving body then it is known as negative acceleration.
Thus, we can conclude that positive acceleration occurs when an object speeds up.
The acceleration that leads to the increase in the speed of the object is called as Positive acceleration.
Explanation:
The acceleration of a body is defined as the amount of change taking place in the magnitude of the velocity of the body in every second. The acceleration of the body is a vector quantity as it requires the direction along with the magnitude of change in the speed of the body.
If the acceleration of the body is acting in the direction opposite to the direction of motion of the body, then the acceleration tends to decrease the speed of the body and it is called as deceleration.
Whereas if the acceleration of a body is in the direction same as that of the direction of motion of the body, then the acceleration of the body increases the speed of the body and this acceleration is termed as the positive acceleration of the body.
Therefore, the acceleration of an object that tends to speed up the object must be acting in the direction same as the direction of motion of the body and therefore it is termed as the positive acceleration of the body.
Thus, The acceleration that leads to the increase in the speed of the object is called as Positive acceleration.
Learn More:
1. Transnational kinetic energy brainly.com/question/9078768.
2. Motion under friction brainly.com/question/7031524.
3. Conservation of momentum brainly.com/question/9484203
Answer Details:
Grade: High School
Subject: Physics
Chapter: Acceleration
Keywords:
acceleration, rate of change, velocity, speed, increase, per second, direction, opposite, motion, along, speed up.
Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=2. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.
Consider the following reaction and associated equilibrium constant:
aA(g)+bB(g)⇌cC(g), Kc = 4.0
The equilibrium concentration of A is [tex]\boxed{\frac{1}{3}}[/tex].
The equilibrium concentration of B is [tex]\boxed{\frac{1}{3}}[/tex].
The equilibrium concentration of C is [tex]\boxed{\frac{2}{3}}[/tex].
Further explanation:
Chemical equilibrium is the state in which the concentration of reactants and products become constant and do not change with time. This is because the rate of forward and backward direction becomes equal. The general equilibrium reaction is as follows:
[tex]{\text{A(g)}}+{\text{B(g)}}\rightleftharpoons{\text{C(g)}}+{\text{D(g)}}[/tex]
The equilibrium constant is the constant that relates the concentration of product and reactant at equilibrium. The formula to calculate the equilibrium constant for the general reaction is as follows:
[tex]{\text{K}}=\dfrac{{\left[ {\text{D}}\right]\left[{\text{C}}\right]}}{{\left[{\text{A}} \right]\left[{\text{B}}\right]}}[/tex]
Here, K is the equilibrium constant.
The given reaction is,
[tex]{\text{aA}}\left( g \right)+{\text{bB}}\left( g \right) \rightleftharpoons{\text{cC}}\left( g \right)[/tex]
Here,
A and B are the two reactants.
C is the product formed.
a and b are the stoichiometric coefficients of A and B respectively.
c is the stoichiometric coefficient of C.
The expression of [tex]{{\text{K}}_{\text{c}}}[/tex] for the above reaction is as follows:
[tex]{{\text{K}}_{\text{c}}}=\dfrac{{{{\left[{\text{C}}\right]}^{\text{c}}}}}{{{{\left[{\text{A}} \right]}^{\text{a}}}{{\left[{\text{B}}\right]}^{\text{b}}}}}[/tex] ...... (1)
Here,
[tex]{{\text{K}}_{\text{c}}}[/tex] is the equilibrium constant that is concentration-dependent.
Let the change in concentration at equilibrium is x. Therefore, the concentration of C becomes x at equilibrium. The concentration of A and B become 1-x at equilibrium.
Substitute x for [C] , 1-x for [A] and 0.57-x for [B], 1 for a, 1 for b and 2 for c in equation (1).
[tex]{{\text{K}}_{\text{c}}}=\dfrac{{{{\left[ {\text{x}} \right]}^2}}}{{{{\left[{{\text{1 - x}}} \right]}^{\text{1}}}{{\left[{{\text{1 - x}}}\right]}^{\text{1}}}}}[/tex] ...... (2)
Rearrange equation (2) and substitute 4 for [tex]{{\text{K}}_{\text{c}}}[/tex] to calculate the value of x.
[tex]{{\text{x}}^2}=\dfrac{{{\text{8x}} - 4}}{3}[/tex]
The final quadratic equation is,
[tex]{\text{3}}{{\text{x}}^2}-8{\text{x}}+4=0[/tex]
Solve for x,
[tex]{\text{x}}={\text{2 , }}\dfrac{2}{3}[/tex]
The value of x equal to 2 is not accepted as it would make the equilibrium concentration of A and B negative, which is not possible. So the value of x comes out to be 2/3.
The equilibrium concentration of [C] is equal to 2/3.
The equilibrium concentration of A is calculated as follows:
[tex]\begin{aligned}\left[ {\text{A}}\right]&=1-\frac{2}{3}\\&=\frac{1}{3}\\\end{aligned}[/tex]
The equilibrium concentration of B is calculated as follows:
[tex]\begin{aligned}\left[ {\text{B}}\right]&=1-\frac{2}{3}\\&=\frac{1}{3}\\\end{aligned}[/tex]
So the equilibrium concentrations of A, B and C are 1/3, 1/3 and 2/3 respectively.
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Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Equilibrium
Keywords: equilibrium constant, A, B, C, a, b, c, 1, 1, 2, 1/3, 1/3, 2/3, Kc, concentration dependent.