Answer: 1.47
Explanation:
The combined gas equation when pressure is constant:
where,
=original number of moles of air in the balloon = ?
= number of moles of air in the heated balloon = ?
= initial volume of gas = 
= final volume of gas = 
= initial temperature of gas = 
= final temperature of gas = 
Now put all the given values in the above equation, we get the final pressure of gas.
Therefore, the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon is 1.47
These are 6 questions and 6 answers.
Question 1:
Answer: 33.7 atm
Explanation:
1) Data:
p=?
m = 1360.0 g N2O
V = 25.0 liter
T = 59.0°C
2) Formulas:
Ideal gas law: p V = n R T
n = mass in grams / molar mass
3) Solution
n = mass of N2O in grams / molar mass of N2O
molar mass of N2O = 2 * 14 g/mol + 16 g/mol = 44 g/mol
n = 1360.0 g / 44 g/mol = 30.9 mol
T = 59.0 + 273.15 K = 332.15 K
R = 0.0821 atm*liter / K*mol
=> p = nRT / V = 30.9 mol * 0.0821 [atm*liter / K * mol] * 332.15K / 25.0 liter = 33.7 atm
Answer: 33.7 atm
Question 2:
Answer: 204.5 liter
Explanaton:
1) Data:
m = 11.7 g of He
V = ?
p = 0.262 atm
T = - 50.0 °C
2) Formulas:
pV = nRT
n = mass in grams / atomic mass
3) Solution:
atomic mass of He = 4.00 g/mol
n = 11.7 g / 4.00 g/mol = 2.925 mol
T = - 50.0 + 273.15 K = 223.15 K
pV = nRT => V = nRT / p
V = 2.925 mol * 0.0821 [* liter / K*mol] *223.15K / 0.262 atm = 204.5 liter
Answer: 204.5 liter
Question 3.
Answer: 97.8 mol
Explanation:
1) Data:
Ethane
T = 15.0 °C
p = 100.0 kPa
V = 245.0 ml
n = ?
2) Formula
pV = nRT
3) Solution
pV = nRT => n = RT / pV
T = 15.0 + 273.15K = 288.15K
R = 8.314 liter * kPa / (mol*K)
n = 8.314 liter * kPa / (mol*K) * 288.15K / [100.0 kPa * 0.245 liter] = 97.8 mol
Answer: 97.8 mol
Question 4:
Answer: 113.67 K = - 159.48 °C
Explanation:
1) Data:
V = 629 ml of O2
p = 0.500 atm
n = 0.0337 moles
T = ?
2) Formula:
pV = nRT
3) Solution:
pV = nRT => T = pV / (nR)
T = 0.500 atm * 0.629 liter / (0.0337 mol * 0.0821 atm*liter/K*mol ) = 113.67 K
°C = T - 273.15 = - 159.48 °C
Question 5.
Answer: 5.61 g
Explanation:
1) Data:
V = 3.75 liter of NO
T = 19.0 °C
p = 1.10 atm
m = ?
2) Formulas
pV = nRT
mass = number of moles * molar mass
3) Solution:
pV = nRT => n = pV / (RT)
T = 19.0 + 273.15 K = 292.15 K
n = 1.10 atm * 3.75 liter / [ (0.0821 atm*liter / K*mol) * 292.15 K ] = 0.17 mol
molar mass of NO = 17.0 g/mol + 16.0 g/mol = 33.0 g/mol
mass = 0.17 mol * 33.0 g/mol = 5.61 g
Question 6:
Answer: 22.4 liter
Explanation:
1) Data:
STP
n = 1.00 mol
V = ?
Solution:
1) It is a notable result that 1 mol of gas at STP occupies a volume of 22.4 liter, so that is the answer.
2) You can calculate that from the formula pV = nRT
3) STP stands for stantard pressure and temperature. That is p = 1 atm and T = 0°C = 273.15 K
4) Clear V from the formula:
V = nRT / p = 1.00 mol * 0.0821 atm*liter / (K*mol) * 273.15 K / 1.00 atm = 22.4 liter
Electromagnetic consists of both electrical and magnetic fields so D. :)
Answer:
P = 1/8
Explanation:
The wave function of a particle in a one-dimensional box is given by:
Hence, the probability of finding the particle in the one-dimensional box is:
Evaluating the above integral from x₁ = 0 to x₂ = L/8 and solving it, we have:
![P = \frac{2}{L} [\frac{L}{16} (1 - 4\frac{sin(\frac{n \pi}{4})}{n \pi})]](https://tex.z-dn.net/?f=%20P%20%3D%20%5Cfrac%7B2%7D%7BL%7D%20%5B%5Cfrac%7BL%7D%7B16%7D%20%281%20-%204%5Cfrac%7Bsin%28%5Cfrac%7Bn%20%5Cpi%7D%7B4%7D%29%7D%7Bn%20%5Cpi%7D%29%5D%20)
Solving for n=4:
I hope it helps you!
