Worksheet: The Ideal Gas Law

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=300K and 𝑃=101.3kPa, and assume that the air behaves as an ideal gas with a molar mass of 0.029 kg/mol.

Q2:

Gaseous boron trifluoride, BF3, is contained in a 4.341 L bulb at 788.0 K at a pressure of 1.220 atm.

How many moles of BF3 is this?

  • A 0.1190 mol
  • B 8 . 1 9 0 Γ— 1 0   mol
  • C 7 . 6 0 0 Γ— 1 0   mol
  • D 1 . 1 9 0 Γ— 1 0   mol
  • E 6 . 5 2 5 Γ— 1 0   mol

How many grams of BF3 is this?

Q3:

A 5.00 L sample of N()2g 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 8.206Γ—10 m3β‹…atm/Kβ‹…mol, how many moles of N()2g are present in this sample?

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

Q4:

If you have 1.55 mol of F()2g 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 8.314Γ—10β‹…/β‹…οŠ±οŠ¨LbarKmol?

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 BaO2 to BaO and O2?

Q6:

What is the volume of oxygen required to burn 12.00 L of ethane gas, CH26, to produce carbon dioxide and water, if the volumes of CH26 and O2 are measured under the same conditions of temperature and pressure and both behave like ideal gases?

Q7:

Lime, CaO, is produced by heating calcium carbonate, CaCO3; 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 metric ton (1.000Γ—10 kg) of calcium carbonate?

  • A 7 . 4 3 Γ— 1 0  L
  • B 5 . 0 2 Γ— 1 0  L
  • C 7 . 4 1 Γ— 1 0 οŠͺ L
  • D 3 . 7 2 Γ— 1 0  L
  • E 9 . 3 8 Γ— 1 0  L

Q8:

The chlorofluorocarbon CClF22 can be recycled into a different compound by reaction with hydrogen to produce CHF()22g, a compound useful in chemical manufacturing:

What volume of hydrogen at 225 atm and 35.5∘C would be required to react with 1.000 metric ton (1.000Γ—10 kg) of CClF22?

  • A 3 . 7 2 Γ— 1 0  L
  • B 1 . 6 6 Γ— 1 0  L
  • C 5 . 0 5 Γ— 1 0 οŠͺ L
  • D 7 . 2 0 Γ— 1 0  L
  • E 2 . 6 6 Γ— 1 0  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 27.0∘C, how many liters of air will such a tank provide to a diver’s lungs (which are at body temperature, 37∘C) at a depth of 20.3 meters 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 expand as the rise, as water evaporates into them.
  • BThe bubbles expand as they rise, because the pressure from the water above decreases.
  • CThe bubbles contract as they dissolve into the water.
  • DThe bubbles stay the same size, because the amount of gas inside is fixed.

Q11:

A 20.0 L cylinder containing 11.34 kg of butane, CH410, 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 27.0∘C?

Q12:

A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25∘C at ground level. What is the volume of the balloon under these conditions?

Q13:

A 10.0-L vessel contains 2.50Γ—10 mol of H2, 1.00Γ—10 mol of He, and 3.00Γ—10οŠͺ mol of Ne at 35.0∘C. Assuming that all three are ideal gases, what is the total pressure in atmospheres?

  • A 111 atm
  • B 9 . 6 1 Γ— 1 0   atm
  • C 974 atm
  • D 1.4 atm
  • E 1 . 0 9 Γ— 1 0   atm

Q14:

Ethanol, CHOH25, is produced industrially from ethylene, CH24, by the following sequence of reactions:

What volume of ethylene at 0.00∘C and 1.00 atm is required to produce 1.000 metric ton (1000 kg) of ethanol if the overall yield of ethanol is 91.0%?

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

Q15:

Propane, CH()38g, is used in gas grills to provide the heat for cooking. What volume of O()2g measured at 25∘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  CO2, 805 g  O2, and 4800 g  N2. At 25∘C, what is the pressure in the cylinder in bar? Assume that all three gases behave as ideal gases under these conditions.

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

Q17:

Gallium reacts with hydrochloric acid to produce hydrogen according to the equation shown. 2Ga()+6HCl()2GaCl()+3H()saqaqg32

What volume of hydrogen at 27∘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 7 . 1 2 Γ— 1 0   mol
  • B 3 . 2 3 Γ— 1 0   mol
  • C 8 . 5 7 Γ— 1 0   mol
  • D 9 . 7 9 Γ— 1 0   mol
  • E 4 . 0 9 Γ— 1 0   mol

Calculate the number of molecules of oxygen in 300 cm3 of air at 237∘C and a pressure of 540 mmHg.

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

Q19:

Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25∘C and 0.993 bar?

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

Q20:

A cylinder of O()2g 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 28.0∘C, what mass of oxygen is in the cylinder?

Q21:

How many liters of HCl gas, measured at 30.0∘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, BF3, 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 BF3 present in the sample.

  • A 1 . 1 9 0 Γ— 1 0   mol
  • B 8 . 1 9 0 Γ— 1 0   mol
  • C 6 . 5 2 5 Γ— 1 0   mol
  • D 1 1 . 9 0 Γ— 1 0   mol
  • E 7 . 6 0 0 Γ— 1 0   mol

Calculate to 3 significant figures the number of grams of BF3 present in the sample.

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