Final answer:
To solve 4cos²(theta) - 3 = 0 within [0, 2pi], isolate the cosine function and find the angles where cos(theta) = ± √3/2. The solutions are theta = 1/6 pi, 5/6 pi, 7/6 pi, and 11/6 pi.
Explanation:
To solve the equation 4cos²((theta) - 3 = 0 for theta in the interval [0, 2pi], we need to follow these steps:
Add 3 to both sides: 4cos²((theta) = 3.Divide both sides by 4: cos2(theta) = 3/4.Take the square root of both sides: cos(theta) = ± √(3/4). This gives us cos(theta) = ± √3/2.Find the angles where the cosine has the values ± √3/2 within the interval [0, 2pi]. These angles are theta = cos-1(√3/2) and theta = cos-1(-√3/2).Since the cosine is positive in the first and fourth quadrants and negative in the second and third quadrants, we get the solutions: theta = 1/6 pi and theta = 5/6 pi for the positive value and theta = 7/6 pi and theta = 11/6 pi for the negative value.The solution to the equation are the angles theta = 1/6 pi, 5/6 pi, 7/6 pi, and 11/6 pi.
Which ionic compound is the most likely to dissolve in water?
CaSO4
Na2SO4
BaSO4
SrSO4
Sodium sulfate (Na2SO4) is the ionic compound most likely to dissolve in water among the options provided.
The student is asking which of the listed ionic compounds is most likely to dissolve in water. Looking at the options, we have Calcium sulfate (CaSO4), Sodium sulfate (Na2SO4), Barium sulfate (BaSO4), and Strontium sulfate (SrSO4). According to solubility rules, most sulfate salts are soluble except for some exceptions, including BaSO4, SrSO4, and CaSO4. Given that sodium compounds are generally highly soluble, Na2SO4 is the compound that is most likely to dissolve in water. This is because there is less size mismatch between the Na+ and SO4(2-) ions compared to the other pairs of ions, which fits the trend that smaller size mismatches lead to greater solubility.
What would make the risk of these cancers even worse for someone who drinks alcohol?
Use the periodic table to answer this question. Decomposing calcium carbonate yields calcium oxide and carbon dioxide. What information is needed to calculate the mass of calcium oxide that can be produced from 4.7 kg of calcium carbonate?
First write and balance the equation, being: CaCO3 - CaO + CO2 Then, using the periodic table, find the molecular masses of CaCO3 and of CaO, finding their ratio. That will be 100g:56g or 0.1kg:0.056kg. Since you have 4.7kg of CaCO3, it corresponds to Xkg of CaO. Making x the subject, it should be X= 4.7*0.056/100=0,002632
Answer : The mass of calcium oxide produced is, 2632 g
Solution : Given,
Mass of calcium carbonate = 4.7 Kg = 4700 g (1 Kg = 1000 g)
Molar mass of calcium carbonate = 100 g/mole
Molar mass of calcium oxide = 56 g/mole
First we have to calculate the moles of calcium carbonate.
[tex]\text{Moles of }CaCO_3=\frac{\text{Mass of }CaCO_3}{\text{Molar mass of }CaCO_3}=\frac{4700g}{100g/mole}=47moles[/tex]
Now we have to calculate the moles of calcium oxide.
The balanced decomposition reaction will be,
[tex]CaCO_3\rightarrow CaO+CO_2[/tex]
From the balanced reaction we conclude that,
As, 1 mole of calcium carbonate decompose to give 1 mole of calcium oxide
So, 47 moles of calcium carbonate decompose to give 47 moles of calcium oxide
Now we have to calculate the mass of calcium oxide.
[tex]\text{Mass of }CaO=\text{Moles of }CaO\times \text{Molar mass of }CaO[/tex]
[tex]\text{Mass of }CaO=(47moles)\times (56g/mole)=2632g[/tex]
Therefore, the mass of calcium oxide produced is, 2632 g
For this question, use the main assumptions of the Kinetic Molecular Theory of gases:
1. Gases are made up of molecules which are relatively far apart.
2. The molecules are in motion at high speeds.
3. The molecular collisions are perfectly elastic.
4. Increase in temperature increases the kinetic energy of the molecules.
Which of the assumptions explains the pressure which a gas exerts?
1
2
3
4
1 and 2
2 and 4 For this question, use the main assumptions of the Kinetic Molecular Theory of gases:
1. Gases are made up of molecules which are relatively far apart.
2. The molecules are in motion at high speeds.
3. The molecular collisions are perfectly elastic.
4. Increase in temperature increases the kinetic energy of the molecules.
Which of the assumptions explains the pressure which a gas exerts?
1
2
3
4
1 and 2
2 and 4
The correct answer is 3. The molecular collisions are perfectly elastic.
Explanation- The rapidly moving particle of gas collides with the walls of the container. All these collision are perfectly elastic. The pressure exerted by the gas is due to this continuous collision and the force experienced per unit area of the walls of the container determines the pressure exerted by the gas.
Assumptions 2 and 3 of the Kinetic Molecular Theory explain gas pressure. High-speed molecular motion causes frequent, perfectly elastic collisions with container walls, generating pressure.
The pressure exerted by a gas can be explained by assumptions 2 and 3 of the Kinetic Molecular Theory.
1. **Assumption 2:** The molecules of a gas are in constant motion at high speeds. This motion creates collisions between the gas molecules and with the walls of the container.
2. **Assumption 3:** The molecular collisions are perfectly elastic. This means that when gas molecules collide with each other or with the walls of the container, there is no net loss of kinetic energy. The total kinetic energy of the system remains constant.
Now, let's delve into the step-by-step explanation of how these assumptions relate to the pressure exerted by the gas:
- When gas molecules collide with the walls of the container, they exert a force on the walls due to the change in momentum. This force per unit area is what we define as pressure.
- The faster the gas molecules are moving (assumption 2), the more forceful these collisions will be.
- Additionally, the more frequently these collisions occur, the greater the pressure will be.
- Since the collisions are perfectly elastic (assumption 3), the molecules rebound from the wall after collision without losing any kinetic energy. This means that each collision contributes equally to the pressure exerted by the gas.
- Therefore, both assumptions 2 and 3 are essential in explaining the pressure exerted by a gas.
So, the correct answer is: **2 and 3**.
In general, atoms react in an attempt to attain the electron configuration of a noble gas.
a. true
b. false
what energy is created when an electron is added to a neutral atom of an element, forming a negative ion?
What changes in the nucleus during nuclear decay by gamma rays A Energy content B Atomic MASS C Atomic number D All of the above.
Final answer:
The correct answer is "atomic mass & atomic number". During nuclear decay by gamma rays, only the energy content of the nucleus changes; atomic mass and atomic number remain constant.
Explanation:
In the process of nuclear decay by gamma rays, there is no change in the atomic mass or atomic number of the nucleus. The only change that occurs during gamma decay is in the energy content of the nucleus. During gamma decay, a nucleus in an excited state drops to a lower energy state by emitting high-energy photons known as gamma rays. This is often represented by the metastable state, labeled with an 'm' next to the mass number. Despite this change in energy, the number of protons (atomic number) and the combined number of protons and neutrons (atomic mass) remain unchanged.
What is the mass of 2 moles of 238 u?
Answer:
Mass of 2 moles of [tex]^{238}\textrm{U}[/tex] is 476.1 g
Explanation:
We know that number of moles of an atom is ratio of mass of the atom to it's atomic weight.Atomic weight of [tex]^{238}\textrm{U}[/tex] is 238.05 g/molSo, mass of 1 mol of [tex]^{238}\textrm{U}[/tex] atom is 238.05 gHence mass of 2 moles of [tex]^{238}\textrm{U}[/tex] = [tex](2mol\times 238.05g/mol)=476.1 g[/tex]Hence mass of 2 moles of [tex]^{238}\textrm{U}[/tex] is 476.1 gWhat is HOFBrINCl, and when do you need to use it?
HOFBrINCl is a mnemonic to remember the seven diatomic molecules: hydrogen, oxygen, fluorine, bromine, iodine, nitrogen, and chlorine, used in Chemistry to balance equations and predict compound formulas.
Explanation:HOFBrINCl is a mnemonic device used in Chemistry to remember the diatomic molecules, which are molecules consisting of two atoms. These seven diatomic molecules are hydrogen (H2), oxygen (O2), fluorine (F2), bromine (Br2), iodine (I2), nitrogen (N2), and chlorine (Cl2). You typically use this mnemonic when you are trying to recall which elements naturally form diatomic molecules, especially when balancing chemical equations or predicting formulas of compounds in Chemistry.
What volume would 3.01•1023 molecules of oxygen gas occupy at STP?
the answer is c) 11.2 L
edge 2021
why are pi bonds weaker than sigma bonds?
A thermometer is placed in water in order to measure the water’s temperature. What would cause the liquid in the thermometer to rise?
The molecules in the water move closer together.
The molecules in the thermometer’s liquid spread apart.
The kinetic energy of the water molecules decreases.
The kinetic energy of the thermometer’s liquid molecules decreases
Answer: Option (b) is the correct answer.
Explanation:
When we use a thermometer to measure the temperature of water then heat from the water will lead to represent an increase in the thermometer reading.
This is because heat or warmth from the water will get transferred to the thermometer as a result, the liquid in the thermometer will also get warm.
Therefore, this warmth will increase kinetic energy of the molecules of liquid in the thermometer. Hence, the liquid will spread.
Thus, we can conclude that the liquid in the thermometer to rise because molecules in the thermometer’s liquid spread apart.
Define element and compound. explain the difference between an element and a compound.
Answer:
Element is a pure substance which cannot be splitted into smaller substances by simple chemical reactions. while Compound is a chemical combination of two or more substances at fixed ratio.
The chemical properties of calcium most similairto the chemical properties of
write the mole ratio of (Mg+2HF➡MgF+H2)
Answer:
Mg+2HF>2MgF+H2
Explanation:
What is a proper adjective?
in general what happens when you increase the temperature of a reaction
I'm kinda in a rush but take your time!Thx! 1.What was Henri Becquerel studying when he accidentally discovered radioactivity?
A.photography B.properties of black light C.properties of X-rays D.solar energy 2.When Marie Curie isolated uranium from pitchblende, she realized that the pitchblende was more radioactive than the uranium she had extracted. What did she conclude about her observations?
A.Pitchblende itself is a radioactive element B.The pitchblende sample contained an unknown radioactive element
C.The pitchblende sample was defective D.Pitchblende should be used as radiation therapy 3.Henri Becquerel's original hypothesis was that fluorescent minerals became excited by a solar energy and gave off X-rays. However, after he discovered uranium minerals emitted their own radiation without the help of solar energy, he abandoned his hypothesis. Why did Becquerel abandon his first hypothesis?
A.He was afraid of ridicule from the scientific community for being wrong
B.He found new evidence that didn't support his original hypothesis
C.He couldn't repeat the results in multiple experiments.
D.He couldn't make the experiment work, so he came up with a new plan
4.Marie Curie had many "firsts". Which of the following is not one of Marie Curie's firsts?
A.first female Nobel Prize winner B.first female professor in the Faculty of Sciences
C.first to suggest that atoms can change D.first to discover X-rays My answers: 1.D 2.B 3.A 4.D
Henri Becquerel was studying the properties of X-rays when he discovered radioactivity. Marie Curie concluded that pitchblende must contain another, more radioactive element upon finding it was more radioactive than its uranium content. Curie was not the first to discover X-rays; that was Roentgen.
Henri Becquerel was studying the properties of X-rays when he accidentally discovered radioactivity. He was experimenting with phosphorescent materials and their ability to produce X-rays after being exposed to sunlight when he observed that uranium salts emitted rays without the need for sunlight, leading to the discovery of radioactivity.
Upon isolating uranium from pitchblende and finding that the pitchblende was more radioactive than the purified uranium, Marie Curie concluded that the pitchblende contained unknown radioactive elements. This led to the discovery of two new elements, polonium, and radium, which were significantly more radioactive than uranium.
Becquerel abandoned his first hypothesis, which postulated that fluorescent minerals excited by solar energy emitted X-rays because he found evidence that uranium emits radiation regardless of exposure to sunlight, thus invalidating his original theory. He adapted his hypothesis based on the evidence he collected that showed uranium's radiation was not dependent on light or fluorescence.
Marie Curie had many firsts in her career, but she was not the first to discover X-rays. That discovery was made by Wilhelm Roentgen in 1895. Marie Curie's notable firsts include being the first female Nobel Prize winner, the first female professor at the Faculty of Sciences at the Sorbonne, and the first person to coin the term radioactivity and suggest that atoms could change as part of radioactive decay.
HELP: MODELING MOLECULES!!!!!!!!!!!!!!!!
How do I solve the electron dot structure, structure formula, and drawing for the following molecules:
Sulfur Hexachloride
Carbon Dioxide
Methyl Cyclohexane
Propane
Ethene
Phenol
What is the bond angle between the hydrogen atoms in an ammonia (NH₃) molecule?
which of the following is an ionic compound h2o brcl mgf2 c2h4 or NH3
Among the given options, MgF2 is an ionic compound.
Explanation:An ionic compound is formed between a metal and a nonmetal. Among the options given, H2O and C2H4 are covalent compounds because they contain only nonmetal elements. NH3 is also a covalent compound because it contains only nonmetals. On the other hand, BrCl is a covalent compound because it contains two nonmetals. Lastly, MgF2 is the correct answer because it contains the metal magnesium (Mg) and the nonmetal fluorine (F). Therefore, MgF2 is an ionic compound.
suppose you found a material in which 12.5% of the original radioactive atoms were present. if the half-life is 47 years, how old is the material?
It can be calculated using the equation: (1/2)ⁿ = x
x - decimal amount remaining,
n - number of half-lives.
x = 12.5% = 12.5%/100% = 0.125
n = ?
(1/2)ⁿ = 0.125
log((1/2)ⁿ) = log(0.125)
n * log(1/2) = log(0.125)
n = log(0.125)/log(1/2) = log(0.125)/log(0.50) = -0.903 / -0.301 = 3
Number of half-lives is 3.
Number of half-lives (n) is quotient of total time elapsed (t) and length of half-life (H).
n = t/H
t = n * H
n = 3
H = 47 years
t = 3 * 47 years = 141 years
As a chlorine atom becomes a negative ion, the atom
(1) gains an electron and its radius increases
(2) gains an electron and its radius decreases
(3) loses an electron and its radius increases
(4) loses an electron and its radius decreases
Answer:
(1) gains an electron and its radius increases
Explanation:
Hello,
Ionization involves the charge of a determined atom in order to form an ion, in this case, the chloride ion which is negative. In such a way, since chloride ion turns out negatively charged via ionization, it is evident that an electron is gained so its radius must increase as result of that gain, therefore, answer is:
(1) gains an electron and its radius increases
As long as a new particle is included into it.
Best regards.
What is the independent variable in the graph? A) Degrees C B) Amount of water Eliminate C) Temperature of water D) Time of heating the water
How many grams of O2 are in 5.0 moles of the oxygen gas?
Answer : The mass of oxygen is 160 grams.
Solution : Given,
Moles of [tex]O_2[/tex] = 5 moles
Molar mass of [tex]O_2[/tex] = 32 g/mole
Formula used :
[tex]\text{ Mass of }O_2=\text{ Moles of }O_2\times \text{ Molar mass of }O_2[/tex]
[tex]\text{ Mass of }O_2=(5moles)\times (32g/mole)[/tex]
[tex]\text{ Mass of }O_2=160g[/tex]
Therefore, 160 grams of [tex]O_2[/tex] are in 5.0 moles of the oxygen gas.
Determine the empirical formula for a compound that is found to contain 10.15 mg P and 34.85 mg Cl.?
But I'm confused because I thought I had to convert 10.15 mg to grams but then I get a huge number if I do that. Why do I leave it as mg?
Final answer:
To determine the empirical formula for a compound containing phosphorus and chlorine, convert mass to grams, calculate moles using molar mass, then find the whole-number ratio of elements. The empirical formula is PCl3.
Explanation:
To determine the empirical formula for a compound containing phosphorus (P) and chlorine (Cl), we first need to convert the mass of each element from milligrams to grams for consistency with molar mass units. The mass of P is 10.15 mg, which equates to 0.01015 g, and the mass of Cl is 34.85 mg, which is 0.03485 g.
Next, we use the molar mass of each element (P: 30.97 g/mol, Cl: 35.45 g/mol) to convert the mass of each element to moles. For P, 0.01015 g × (1 mol / 30.97 g) = 0.0003277 mol. For Cl, 0.03485 g × (1 mol / 35.45 g) = 0.0009830 mol.
To find the whole-number ratio, we divide the moles of each element by the smallest number of moles obtained from the calculation:
P: 0.0003277 / 0.0003277 = 1Cl: 0.0009830 / 0.0003277 ≈ 3Therefore, the empirical formula for the compound is P1Cl3.
Methane, CH4, burns in oxygen gas to form water and carbon dioxide. What is the correct balanced chemical equation for this reaction?
I'm having a hard time understanding how to balance a chemical equation. I'm really not sure how to even begin. Please help!
Household hazardous waste can be eliminated by preparing your own cleaning products using the following ingredients EXCEPT: vinegar bicarbonate soda cornstarch Windex
I think the correct answer from the choices listed above is the last option. Household hazardous waste can be eliminated by preparing your own cleaning products using the following ingredients except Windex.
It is a chemical product that is hazardous.
Explanation:
Windex may be a glass and hard-surface cleaner. Windex was unreal by the Drackett Company in 1933 and has been marketed throughout.Windex cannot be used.
Windex is the ingredient that should not be used for preparing non-toxic, homemade cleaning products. Vinegar, baking soda, and cornstarch are all safe alternatives that can effectively clean and reduce household hazardous waste when used in homemade cleaning solutions.
The student's question pertains to the elimination of household hazardous waste by preparing one's own cleaning products. Among the ingredients listed, vinegar, bicarbonate soda (baking soda), and cornstarch are common safe household ingredients used for cleaning purposes. However, Windex is a commercial product which often contains chemicals and is not a suitable ingredient for making your own non-toxic, homemade cleaning products.
Homemade cleaning solutions, such as a mixture of vinegar and baking soda, can serve as effective alternatives to reduce the presence of hazardous substances in the household. These natural products are not only eco-friendly, but also pose less risk to personal health compared to some commercially available cleaners.
How many atoms of oxygen are represented in 2Fe(NO3)2?
3
6
12
18
Answer : The number of atoms of oxygen present in [tex]2Fe(NO_3)_2[/tex] are, 12.
Explanation :
As we know that, [tex]Fe(NO_3)_2[/tex] is made up of the combination of iron and nitrate molecule.
In [tex]2Fe(NO_3)_2[/tex] compound, there are three elements which are iron (Fe), nitrogen (N) and oxygen (O).
The number of atoms of iron = 2
The number of atoms of nitrogen = 4
The number of atoms of oxygen = 12
Hence, the number of atoms of oxygen present in [tex]2Fe(NO_3)_2[/tex] are, 12.
4Fe+3O2
I really have no idea how to do this.. HELP