Ch.6 - Gases

Problem 107a

Previous problem

Next problem

Chapter 6, Problem 107a

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. Calculate the mass of air in an air-filled tire.

Verified step by step guidance

Convert the volume of the tire from milliliters to liters by dividing by 1000.

Convert the pressure from psi to atm using the conversion factor: 1 atm = 14.7 psi.

Convert the temperature from Celsius to Kelvin by adding 273.15.

Use the ideal gas law, PV = nRT, to solve for the number of moles (n) of air in the tire. Use R = 0.0821 L·atm/mol·K.

Calculate the mass of air by multiplying the number of moles of air by the average molar mass of air (28.8 g/mol).

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the properties of gases under various conditions. In this scenario, it will help determine the number of moles of air and helium in the tire based on the given pressure, volume, and temperature.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a gas and the number of moles. In this question, the average molar mass of air (28.8 g/mol) is used to calculate the mass of air in the tire after determining the number of moles using the Ideal Gas Law.

Gas Density

Gas density is defined as the mass of gas per unit volume, often expressed in grams per liter (g/L). Understanding gas density is important for comparing the masses of different gases in the same volume. In this case, knowing the density of air and helium will allow for the calculation of their respective masses in the tire, highlighting the advantages of using helium for weight reduction.

Recommended video:

Gas Density Example

Related Practice

Consider the reaction:

2 SO₂(g) + O₂(g) → 2 SO₃(g)

a. If 285.5 mL of SO₂ reacts with 158.9 mL of O₂ (both measured at 315 K and 50.0 mmHg), what is the limiting reactant and the theoretical yield of SO₃?

1299

views

Textbook Question

Ammonium carbonate decomposes upon heating according to the balanced equation: (NH₄)₂CO₃(s) → 2 NH₃(g) + CO₂(g) + H₂O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.

7704

views

Textbook Question

Ammonium nitrate decomposes explosively upon heating according to the balanced equation: 2 NH4NO3(s)¡2 N2( g) + O2( g) + 4 H2O( g) Calculate the total volume of gas (at 125 °C and 748 mmHg) produced by the complete decomposition of 1.55 kg of ammonium nitrate.

7865

views

Textbook Question

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. Calculate the mass of helium in a helium-filled tire.

An ordinary gasoline can measuring 30.0 cm by 20.0 cm by 15.0 cm is evacuated with a vacuum pump. Assuming that virtually all of the air can be removed from inside the can and that atmospheric pressure is 14.7 psi, what is the total force (in pounds) on the surface of the can? Do you think that the can could withstand the force?

1057

views