Methodology
Problem One
What is the effective volume of a gaseous methane molecule at STP?
Step #1. What is the volume of one mole of a gas at STP?
press for answer
22.4 L
Step #2. What is standard pressure and temperature?
press for answer
One atmosphere and 0 °C (273 K)
Step #3. How many molecules of methane are there in 22.4 L at STP?
press for answer
6 x 1023 molecules
Step #4. What is the effective volume of one molecule?
press for answer
22.4 L/ 6 x 1023 molecules = 4 x 10-23 L
Step #5. Express this volume in cubic centimeters.
press for answer
One liter is 1000 cm3. Thus, the volume is:
4 x 10-23 L x 1000 cm3/L = 4 x 10-20 cm3
Step #6. Our term "effective" volume is useful because it gives some idea of how much space can be a assigned to a molecule in the gaseous state. Is a molecule confined to this space?
press for answer
No, each and every molecule can move throughout the entire container. The effective volume is the space each molecule would occupy if it did not move about through the container.
Step #7. What is the effective volume of methane in the liquid state (assume a density of 0.8 g/mL)?
press and hold for answer
One mole of liquid methane has a volume of:
16 g / 0.8 g/mL = 20 mL = 20 cm3. Thus:
20 cm3 / 6 x 1023 molecules = 3 x 10-23 cm3/molecule
Problem Two
At a certain temperature, 1.0 L of a gas has a pressure of 760 torr. What will the volume be if the pressure changes to 380 torr?
Step #1. What are the four variables that we use to measure a sample of gas?
press for answer
volume, pressure, temperature, and number of moles
Step #2. What is the relationship between volume and pressure?
press for answer
If the temperature and number of moles remain constant, volume is inversely proportional to pressure.
Step #3. Qualitatively, if the pressure of a gas increases (at constant temperature and number of moles), what happens to the volume?
press for answer
the volume decreases
Step #4. If the pressure doubles, how much will the volume decrease?
press for answer
If the pressure goes up by a factor of 2, the volume will decrease by a factor of 2.
Step #5. For our 1.0 L sample of gas, what will the new volume be?
press and hold for answer
760 torr / 380 torr x 1.0 L = 2.0 L
Problem Three
The indirect proportionality between volume and temperature can be expressed as:
V µ 1/P
Step #1. Write this as an equation.
press for answer
V = k/P
Step #2. For the gas in question 2, what is the value of k?
press for answer
Using the fact that 1.0 L is the volume at 760 torr,
V = k/P = 1.0 L = k/760 torr, or,
k = 760 L-torr.
Step #3. Use this value of k to calculate the volume at 380 torr
press for answer
V = 760 L-torr/P = 760 L-torr/380 torr = 2.0 L
Step #4. What factors will affect the value of k?
press and hold for answer
the number of moles of gas and its temperature.
Problem Four
What pressure is required to change the volume of a gas at constant temperature from 2.0 L at 1.0 atm to 0.50 L?
Step #1. What is the relationships between volume and pressure?
press for answer
V = k/P. They are indirectly proportional.
Step #2. If the volume decreases by a factor of 4, what will happen to the pressure?
press for answer
It will increase by a factor of 4.
Step #3. What pressure is required to change from a volume of 2.0 L at 1.0 atm to 0.50 L?
press and hold for answer
2.0 L / 0.50 L x 1.0 atm = 4.0 atm
Problem Five
A 1.0 g sample of gas occupies a volume of 1.0 L at a temperature of 0 °C. What volume will it occupy at a temperature of 50 °C if it is maintained at a constant pressure?
Step #1. What variables are changing in this problem?
press for answer
volume and temperature
Step #2. What is the relationship between volume and temperature?
press for answer
Volume is directly proportional to absolute temperature.
Step #3. What percentage does the absolute temperature increase in this problem?
press for answer
50 K / 273 K = 0.18, or 18%
Step #4. What percentage will the volume increase?
press for answer
18%
Step #5. What is the volume at 50 °C?
press and hold for answer
323 K / 273 K x 1.0 L = 1.18 L
This is an 18% increase in volume.
Problem Six
A 10 L sample of a gas is at a pressure of 500 torr and 100 °C. If the volume is kept constant at 10 L, what temperature will produce a pressure of 760 torr?
Step #1. What variables are changing in this problem?
press for answer
temperature and pressure
Step #2. What is the relationship between temperature and pressure at constant volume?
press for answer
The pressure is directly proportional to the absolute temperature.
Step #3. By what factor must the absolute temperature increase in order to produce a pressure change from 500 torr to 760 torr?
press for answer
760 torr / 500 torr = 1.52
Step #4. Calculate the temperature required.
press and hold for answer
(760 torr / 500 torr) x 373 K = 567 K
Problem Seven
A 10 L sample of a gas is at a pressure of 500 torr and 100 °C. What will the volume be at a pressure of 760 torr and 0.0 °C?
Step #1. What variables are changing in this problem?
press for answer
volume, temperature, and pressure
Step #2. In previous problems, only two variables were changing. How do we deal with three?
press for answer
Specifically, we will first change the temperature and look at the change in volume, and then apply the pressure change to the new volume.
Step #3. How will the volume of 10 L be affected by a change from 100 °C to 0 °C?
press for answer
(10 L x 273 K) / 373 K = 7.3 L
Step #4. How will this volume of 7.3 L be affected by a change from 500 torr to 760 torr?
press and hold for answer
7.3 L x (500 torr / 760 torr) = 4.8 L
Problem Eight
A 10 L sample of a gas is at a pressure of 500 torr and 100 °C. How many moles of gas are present?
Step #1. What variable is unknown?
press for answer
n, the number of moles
Step #2. When three of the four variables are known, how do we find the fourth?
press for answer
by using the ideal gas equation, PV = nRT
Step #3. If R = 0.0821 L-atm/K-mole, then volume must be in units of liters, pressure in atmospheres, temperature in K. Solve for n.
press and hold for answer
n = PV/RT
= (500 torr/760 torr)(10 L) (0.0821 L-atm/K-mole)(373 K)
= 0.21 moles
Problem Nine
What pressure is required to produce a volume of 10 L at 100 °C for a sample of 1.6 g of methane (CH4)?
Step #1. How many moles of methane are we dealing with?
press for answer
1.6 g / 16 g/mole = 0.10 mole
Step #2. Solve the ideal equation for P
press for answer
PV = nRT, P = nRT/V
Step #3. Determine the pressure
press for answer
P = nRTV = (0.10 mole)(0.0821 L-atm/K-mole)(373 L)10 L = 0.31 atm
Step #4. Express the pressure in torr
press and hold for answer
0.31 atm x 760 torr/atm = 233 torr
Problem Ten
What is the molecular weight of a 1.23 g sample of a gas that occupies a volume of 1.28 L at a temperature of 730 torr and 10.5 °C?
Step #1. Determine the number of moles of gas using the ideal gas equation.
press for answer
PV = nRT
n = PVRT
= (730 torr/760 torr)(1.28 L)(0.0821 L-atm/K-mole)(283.5 K)
= 0.0528 moles
Step #2. How much does this 0.053 moles weigh?
press for answer
1.23 g
Step #3. What is the molecular weight?
press and hold for answer
1.23 g / 0.053 moles = 23.3 g/mole
Problem Eleven
What is the molecular weight of a gas with a density of 2.09 g/L at 500 torr and 200 K?
Step #1. The density provides the mass of one liter. Calculate the number of moles of gas in one liter.
press for answer
n = PVRT
= (500 torr,760 torr)(1.00 L)(0.0821 L-atm/K-mole)(200 K)
= 0.040 moles
Step #2. What is the mass of this number of moles?
press for answer
2.09 g
Step #3. What is the molar mass (molecular weight)?
press and hold for answer
2.09 g 0.040 moles = 52 g/mole
Problem Twelve
A 0.2 mole sample of N2 is mixed with 0.4 mole of O2 at a total pressure of 2 atm. What is the partial pressure of N2?
Step #1. Determine the mole fraction of N2.
press for answer
0.2 mole / 0.6 mole = 0.33
Step #2. Determine the partial pressure of N2.
press and hold for answer
P = 0.33 x 2 atm = 0.66 atm