Worksheet: The Ideal Gas Law

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In this worksheet, we will practice using the ideal gas law, which relates the pressure, volume, quantity, and temperature of an ideal gas.

Q1:

If a person breathes at a rate of 14 respirations per minute, and each respiration involves 0.5 dm3 of air, what will be the total mass of air breathed in a day? (Take 𝑇 = 3 0 0 K and 𝑃 = 1 0 1 . 3 k P a , and assume that the air behaves as an ideal gas with a molar mass of 0.029 kg/mol).

Q2:

Gaseous boron trifluoride, B F 3 , is contained in a 4.341-L bulb at 788.0 K at a pressure of 1.220 atm.

How many moles of B F 3 is this?

  • A 0.1190 mol
  • B 7 . 6 0 0 Γ— 1 0 βˆ’ 2 mol
  • C 6 . 5 2 5 Γ— 1 0 βˆ’ 2 mol
  • D 8 . 1 9 0 Γ— 1 0 βˆ’ 2 mol
  • E 1 . 1 9 0 Γ— 1 0 βˆ’ 3 mol

How many grams of B F 3 is this?

  • A 5.553 g
  • B 87.97 g
  • C 11.43 g
  • D 6.563 g
  • E 55.72 g

Q3:

A 5.00 L sample of N ( ) 2 g is held at a pressure of 2.00 atm and a temperature of 315 K. Assuming ideal-gas behavior and a value for the gas constant of 8 . 2 0 6 Γ— 1 0 βˆ’ 5 m3β‹…atm/Kβ‹…mol, how many moles of N ( ) 2 g are present in this sample?

  • A 0.208 mol
  • B 2.69 mol
  • C 0.004 mol
  • D 0.387 mol

Q4:

If you have 1.55 mol of F ( ) 2 g at 1.12 bar pressure and a temperature of 0 ∘ C , what is the volume of this gas sample, assuming ideal-gas behavior and a value of the gas constant of 8 . 3 1 4 Γ— 1 0 β‹… / β‹… βˆ’ 2 L b a r K m o l ?

Q5:

What volume of oxygen at 423.0 K and a pressure of 127.4 kPa is produced by the decomposition of 129.7 g of B a O 2 to B a O and O 2 ?

Q6:

What is the volume of oxygen required to burn 12.00 L of ethane gas, C H 2 6 , to produce carbon dioxide and water, if the volumes of C H 2 6 and O 2 are measured under the same conditions of temperature and pressure and both behave like ideal gases?

Q7:

Lime, , is produced by heating calcium carbonate, ; carbon dioxide is the other product. What volume of carbon dioxide at 875 K and 0.966 atm is produced by the decomposition of 1 tonne ( kg) of calcium carbonate?

  • A L
  • B L
  • C L
  • D L
  • E L

Q8:

The chlorofluorocarbon can be recycled into a different compound by reaction with hydrogen to produce , a compound useful in chemical manufacturing:

What volume of hydrogen at 225 atm and would be required to react with 1.000 tonne ( kg) of ?

  • A L
  • B L
  • C L
  • D L
  • E L

Q9:

When filled with air, a typical scuba tank with a volume of 13.2 L has a pressure of 153 atm. If the water temperature is , how many liters of air will such a tank provide to a diver’s lungs (which are at body temperature, ) at a depth of 20.3 metres in the ocean where the pressure is 3.13 atm?

Q10:

How and why does the volume of the bubbles exhausted by a scuba diver change as they rise to the surface, assuming that they remain intact?

  • AThe bubbles contract as they dissolve into the water.
  • BThe bubbles expand as the rise, as water evaporates into them.
  • CThe bubbles stay the same size, because the amount of gas inside is fixed.
  • DThe bubbles expand as they rise, because the pressure from the water above decreases.

Q11:

A 20.0 L cylinder containing 11.34 kg of butane, C H 4 1 0 , was opened to the atmosphere. What would be the mass of the remaining gas in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.983 atm, at a temperature of 2 7 . 0 ∘ C ?

Q12:

A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 2 5 ∘ C at ground level. What is the volume of the balloon under these conditions?

Q13:

A 10.0-L vessel contains 2 . 5 0 Γ— 1 0 βˆ’ 3 mol of H 2 , 1 . 0 0 Γ— 1 0 βˆ’ 3 mol of H e , and 3 . 0 0 Γ— 1 0 βˆ’ 4 mol of N e at 3 5 . 0 ∘ C . Assuming that all three are ideal gases, what is the total pressure in atmospheres?

  • A 111 atm
  • B 974 atm
  • C 1 . 0 9 Γ— 1 0 βˆ’ 3 atm
  • D 9 . 6 1 Γ— 1 0 βˆ’ 3 atm
  • E 1.4 atm

Q14:

Ethanol, C H O H 2 5 , is produced industrially from ethylene, C H 2 4 , by the following sequence of reactions:

What volume of ethylene at 0 . 0 0 ∘ C and 1.00 atm is required to produce 1.000 metric ton ( 1 0 0 0 kg) of ethanol if the overall yield of ethanol is 9 1 . 0 % ?

  • A 2 . 3 0 Γ— 1 0 6 L
  • B 1 . 1 2 Γ— 1 0 5 L
  • C 6 . 2 9 Γ— 1 0 5 L
  • D 5 . 3 5 Γ— 1 0 5 L
  • E 9 . 9 6 Γ— 1 0 5 L

Q15:

Propane, C H ( ) 3 8 g , is used in gas grills to provide the heat for cooking. What volume of O ( ) 2 g measured at 2 5 ∘ C and 1 atm is required to react with 2.7 L of propane measured under the same conditions of temperature and pressure? Assume that the propane undergoes complete combustion and use a value for 𝑅 of 8.314 J/molβ‹…K.

Q16:

A 36.0 L cylinder of a gas used for calibration of blood gas analyzers in medical laboratories contains 350 g   C O 2 , 805 g  O 2 , and 4 8 0 0 g  N 2 . At 2 5 ∘ C , what is the pressure in the cylinder in bar? Assume that all three gases behave as ideal gases under these conditions.

  • A 168 bar
  • B 101 bar
  • C 300 bar
  • D 141 bar
  • E 67.8 bar

Q17:

Gallium reacts with hydrochloric acid to produce hydrogen according to the equation

What volume of hydrogen at 2 7 ∘ C and 723 torr may be prepared by the reaction of 8.88 g of gallium with an excess of hydrochloric acid?

Q18:

Air contains 20.95% oxygen by volume.

Calculate the number of moles of oxygen in 1.00 L of air at 298 K and a pressure of 1.00 atm.

  • A 3 . 2 3 Γ— 1 0 βˆ’ 2 mol
  • B 7 . 1 2 Γ— 1 0 βˆ’ 2 mol
  • C 4 . 0 9 Γ— 1 0 βˆ’ 2 mol
  • D 8 . 5 7 Γ— 1 0 βˆ’ 3 mol
  • E 9 . 7 9 Γ— 1 0 βˆ’ 3 mol

Calculate the number of molecules of oxygen in 300 cm3 of air at 2 3 7 ∘ C and a pressure of 540 mmHg.

  • A 6 . 4 2 Γ— 1 0 2 0
  • B 6 . 6 0 Γ— 1 0 2 1
  • C 1 . 2 7 Γ— 1 0 2 0
  • D 2 . 4 2 Γ— 1 0 2 1
  • E 4 . 8 8 Γ— 1 0 2 0

Q19:

Methane, C H 4 , is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of C H 4 . What is the volume of this much methane at 2 5 ∘ C and 0.993 bar?

  • A 8 5 . 5 Γ— 1 0 3 L
  • B 1 . 2 6 Γ— 1 0 3 L
  • C 1 . 0 2 Γ— 1 0 4 L
  • D 1 . 0 2 Γ— 1 0 3 L
  • E 8 . 5 5 Γ— 1 0 4 L

Q20:

A cylinder of O ( ) 2 g used in breathing by emphysema patients has a volume of 3.00 L at a pressure of 10.0 atm. If the temperature of the cylinder is 2 8 . 0 ∘ C , what mass of oxygen is in the cylinder?

Q21:

How many liters of H C l gas, measured at 3 0 . 0 ∘ C and 1.00 bar, are required to prepare 1.25 L of 3.20 M hydrochloric acid?

Q22:

A pure sample of boron trifluoride, B F 3 , is contained in a 4.341 L bulb at 788.0 K, at a pressure of 1.220 atm.

Calculate to 4 significant figures the number of moles of B F 3 present in the sample.

  • A 0.1190 mol
  • B 7 . 6 0 0 Γ— 1 0 βˆ’ 2 mol
  • C 6 . 5 2 5 Γ— 1 0 βˆ’ 2 mol
  • D 8 . 1 9 0 Γ— 1 0 βˆ’ 2 mol
  • E 1 . 1 9 0 Γ— 1 0 βˆ’ 3 mol

Calculate to 3 significant figures the number of grams of B F 3 present in the sample.

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