Dalton's and Boyle's Law practice

Question

1. A metal tank contains three gases: oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 35 atm of O2, 5 atm of N2, and 25 atm of He, what is the total pressure inside of the tank?

1. Blast furnaces give off many unpleasant and unhealthy gases. If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen sulfide is 0.02 atm, what is the partial pressure of the remaining air?

1.  Which is NOT a value equal to 1 atm of pressure?

a.	760 torr	c.	101.3 kPa
b.	1 psi	d.	760 mmHg

1. A sample of three mixed gases is at 632.0 mm Hg. If the partial pressure of CO2 is 124.3 mm Hg and the partial pressure of N2 is 461.9 mm Hg, what is the partial pressure of O2?

1. A mixture of oxygen, hydrogen, and water vapor has a total pressure of 684 mm Hg. The partial pressure of oxygen is 380 mm Hg and that of hydrogen is 0.100 atm. What is the partial pressure of water vapor?

Boyle’s Law P1V1=P2V2

1. If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?

2) I have added 15 L of air to a balloon at sea level (1.0 atm). If I take the balloon with me to Denver, where the air pressure is 0.85 atm, what will the new volume of the balloon be?

1. I’ve got a car with an internal volume of 12,000 L. If I drive my car into the river and it implodes, what will be the volume of the gas when the pressure goes from 1.0 atm to 1.4 atm?

1. The air in a syringe has volume 25.0 mL when the pressure is 4.38 atm. What will be the volume when the pressure is 0.65 atm?

1. A sample of carbon dioxide occupies a volume of 3.50 liters of 125 kPa pressure. What pressure would the gas exert if the volume was decreased to 2.00 liters?

Answer 1

All of these run on one equation — Dalton's law of partial pressures:

P_total = P₁ + P₂ + P₃ + ...

Each gas exerts pressure as though the others were not there, so the partial pressures simply add. Some questions give you the parts and want the total; others give the total and want a missing part. Same equation either way.

1. Metal tank with O₂, N₂, He

P_total = 35 + 5 + 25 = 65 atm

2. Blast furnace — remaining air

P_remaining = 0.99 − 0.05 − 0.02 = 0.92 atm

3. Which is NOT equal to 1 atm?

Answer: b, 1 psi.

One atmosphere equals 14.7 psi, not 1. The others are all correct definitions: 760 torr, 760 mmHg, and 101.3 kPa (torr and mmHg are the same unit under two names).

That 14.7 figure is worth knowing outside class — it is why car tyres at about 32 psi hold roughly two atmospheres above the surrounding air.

4. Partial pressure of O₂

P(O₂) = 632.0 − 124.3 − 461.9 = 45.8 mm Hg

5. Partial pressure of water vapour — the one with a trap

Notice that hydrogen is given in atm while everything else is in mm Hg. You cannot subtract until the units match:

P(H₂) = 0.100 atm × 760 mm Hg/atm = 76.0 mm Hg

P(H₂O) = 684 − 380 − 76.0 = 228 mm Hg

Subtracting 0.100 directly would give 304 — a clean-looking number that is completely wrong. Whenever a problem mixes pressure units, that mixing is deliberate.

Summary: 65 atm · 0.92 atm · b · 45.8 mm Hg · 228 mm Hg

Why partial pressures add at all: in an ideal gas the molecules do not interact and their own volume is negligible, so each species contributes pressure in proportion to how many molecules it has, regardless of what else is present. That is also why P_gas = X_gas × P_total works — partial pressure and mole fraction are the same ratio expressed two ways.