#1 - 10

**Problem #1:** Determine the volume of occupied by 2.34 grams of carbon dioxide gas at STP.

**Solution:**

1) Rearrange PV = nRT to this:

V = nRT / P

2) Substitute:

V = [ (2.34 g / 44.0 g mol¯^{1}) (0.08206 L atm mol¯^{1}K¯^{1}) (273.0 K) ] / 1.00 atmV = 1.19 L (to three significant figures)

**Problem #2:** A sample of argon gas at STP occupies 56.2 liters. Determine the number of moles of argon and the mass in the sample.

**Solution:**

1) Rearrange PV = nRT to this:

n = PV / RT

2) Substitute:

n = [ (1.00 atm) (56.2 L) ] / [ (0.08206 L atm mol¯^{1}K¯^{1}) (273.0 K) ]n = 2.50866 mol (I'll keep a few guard digits)

3) Multiply the moles by the atomic weight of Ar to get the grams:

2.50866 mol times 39.948 g/mol = 100. g (to three sig figs)

**Problem #3:** At what temperature will 0.654 moles of neon gas occupy 12.30 liters at 1.95 atmospheres?

**Solution:**

1) Rearrange PV = nRT to this:

T = PV / nR

2) Substitute:

T = [ (1.95 atm) (12.30 L) ] / [ (0.654 mol) (0.08206 L atm mol¯^{1}K¯^{1}) ]T = 447 K

**Problem #4:** A 30.6 g sample of gas occupies 22.414 L at STP. What is the molecular weight of this gas?

**Solution:**

Since one mole of gas occupies 22.414 L at STP, the molecular weight of the gas is 30.6 g mol¯^{1}

**Problem #5:** A 40.0 g gas sample occupies 11.2 L at STP. Find the molecular weight of this gas.

**Solution:**

11.2 L at STP is one-half molar volume, so there is 0.500 mol of gas present. Therefore, the molecular weight is 80.0 g mol¯^{1}

**Problem #6:** A 12.0 g sample of gas occupies 19.2 L at STP. What is the molecular weight of this gas?

**Solution:**

This problem, as well as the two just above can be solved with PV = nRT. You would solve for n, the number of moles. Then you would divide the grams given by the mole calculated.

1) Use PV = nRT:

(1.00 atm) (19.2 L) = (n) (0.08206) (273 K)n = 0.8570518 mol (I'll keep a few guard digits)

2) Determine the molecular weight:

12.0 g / 0.8570518 mol = 14.0 g/mol

3) Since it is at STP, we can also use molar volume:

(19.2 L / 12.0 g) = (22.414 L / x )19.2x = 268.968

x = 14.0 g/mol

Warning: you can only use molar volume when you are at STP.

**Problem #7:** 96.0 g. of a gas occupies 48.0 L at 700.0 mm Hg and 20.0 °C. What is its molecular weight?

**Solution:**

1) Solve for the moles using PV = nRT:

n = PV / RTn = [ (700.0 mmHg / 760.0 mmHg atm¯

^{1}) (48.0 L) ] / [ (0.08206 L atm mol¯^{1}K¯^{1}) (293.0 K) ]n = 1.8388 mol

2) Divide the grams given (96.0) by the moles just calculated above:

96.0 g / 1.8388 mol = 52.2 g/mol

**Problem #8:** 20.83 g of a gas occupies 4.167 L at 79.97 kPa at 30.0 °C. What is its molecular weight?

**Solution:**

1) Solve for the moles using PV = nRT:

n = PV / RTn = [ (79.97 kPa / 101.325 kPa atm¯

^{1}) (4.167 L) ] / [ (0.08206 L atm mol¯^{1}K¯^{1}) (303.0 K) ]n = 0.13227 mol

2) Divide the grams given (20.83) by the moles just calculated above:

20.83 g / 0.13227 mol = 157.5 g/mol

Notice that, in the two problems just above, the I converted the pressure unit given in the problem to atmospheres. I did this to use the value for R that I have memorized. There are many different ways to express R, it's just that L-atm/mol-K is the unit I prefer to use, whenever possible.

Also, you cannot use molar volume since the two problems just above are not at STP.

**Problem #9:** What is the value of and units on R? What is R called ("A letter" is not the correct answer!)?

R is called the gas constant. It was first discovered, as part of the discovery in the mid-1830's by Emil Clapeyron of what is now called the Ideal Gas Law.Sometimes it is called the universal constant because it shows up in many non-gas-related situations. However, it is mostly called the gas constant.

Depending on the units selected, the "value" for R can take on many different forms. Here is a list. Keep in mind these different "values" represent the same thing.

**Problem #10:** 5.600 g of solid CO_{2} is put in an empty sealed 4.00 L container at a temperature of 300 K. When all the solid CO_{2} becomes gas, what will be the pressure in the container?

**Solution:**

1) Determine moles of CO_{2}:

5.600 g / 44.009 g/mol = 0.1272467 mol

2) Use PV = nRT

(P) (4.00 L) = (0.1272467 mol) (0.08206) (300 K)P = 0.7831 atm (to four sig figs)