Chapter 8: gas laws

Question 1

Ideal gas law?

Answer 1

PV = nRT
p = pressure (atm)
- 760.0 torr = 1 atm
v = volume (in LITERS)
- 1000 ml = 1 L
n = moles
- make sure to convert grams of the substance to moles of the substance
- r = gas constant (0.08205 liter * atm/ mole * K)
t = temperature (kelvin)
- k = c + 273.2

Question 2

How do you determine if a factor in the ideal gas law (PV = nRT) will increase/decrease when another factor increases/decreases?

Answer 2

Make sure the right side equals the left side. If something on the left side increases/decreases, something on the right must increase/decrease by a value that will make both sides equal
- make sure to cancel out constants
EX: if we half the volume of the cylinder and double the number of moles of gas, and keep the temperature constant, what will happen to the pressure of the system?
PV = nRT
v = decreases by 1/2
n = doubles by 2
P must increase by 4, since 1/2 * 4 = 2, which is even with n =2.

Question 3

How to solve a “2 state problem”?

Answer 3

Make of list of things that are in the first state of the gas and the second state of the gas. Cancel out anything that stays constant. Cross multiply to solve for the variable you’re trying to find.
EX:
State 1 State 2
p = 1.00 atm p = 1.00 atm
v1 = 24.5 liters v2 = ?
n1 = 1.00 mol n2 = 5.00 mol
T1 = 25.6 C T2 = -50.00 C
Use the formula:
P1V1 / N1T1 = P2V2 / N2T2
Cross multiply to get V2 = T2/T1 * N2/N1 * V1
Substitute numbers in:
223.2 K/298.2 K * 5.00 mol/1.00 mol * 24.5L
= 91.7L

Question 4

How to solve for GMM of a gas/vapor given mass?

Answer 4

Find the number of moles of the gas using the equation n = PV/RT, then divide grams of the vapor by moles of the vapor
GMM = grams of vapor / moles of vapor

Question 5

Formula to calculate GMM from distance the gas migrates in a fixed time relative to a known gas?

Answer 5

(Distance A/Distance B) = (GMMb/GMMa)1/2
- use this formula to find gmm of unknown gas

Question 6

How to calculate partial pressure?

Answer 6

P total = PPa + PPb + PPc
Ptotal = total pressure exerted by these gases
Ppa = pressure of gas A
PPb = pressure of gas B
PPc = pressure of gas C
EX: A storage tank contains 2 moles of Ar, 3 moles of O2, and 5 moles of N2 at a total pressure of 1000 torr. Calculate the partial pressure of each gas.
Step 1: Calculate mole fraction of each gas
Mole fraction (X) = n Gas/ nTotal
nT = 2 + 3 + 5 = 10
X Ar = nAr/nT = 2/10 = 1/5 = 0.2
X O2 = 3/10 = 0.3
X N2 = 5/10 = 1/2 = 0.5
Step 2: Multiply mole fraction by total pressure to get partial pressure of the gas
P Ar = X Ar * PT = 0.2 (1000) = 200 torr
P O2 = 0.3 (1000) = 300 torr
P N2 = 0.5 (1000) = 500 torr
Step 3: Check your work. Add up the partial pressures, they should equal the total pressure.
500 + 300 + 200 = 1000

Question 7

How to find GMM of gas from “u” value?

Answer 7

u = (3RT/ GMM)^1/2
- manipulate the equation to find GMM

Question 8

How to find partial pressure and total pressure (using PV = nRT)?

Answer 8

Manipulate the equation to solve for p:
P = nRT/V
If gas is given in grams, divide by molar mass to find moles of the gas
After finding the moles of the gas, substitute R, T and V and solve for P.
- Do this for every gas given.
Add the partial pressure of the gases up to get the total pressure.