A typical high-pressure tire on a bicycle might have a volume of 365 mL and a pressure of 7.80 atm at 25 °C. Suppose the rider filled the tire with helium to minimize weight. What is the mass of the helium in the tire?

Verified step by step guidance

Convert the volume from milliliters to liters by dividing by 1000, since 1 L = 1000 mL.

Use the ideal gas law equation, \( PV = nRT \), to solve for the number of moles \( n \) of helium. Here, \( P \) is the pressure in atm, \( V \) is the volume in liters, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Rearrange the ideal gas law equation to solve for \( n \): \( n = \frac{PV}{RT} \). Substitute the known values for \( P \), \( V \), \( R \), and \( T \) into the equation to find \( n \).

Calculate the mass of helium by multiplying the number of moles \( n \) by the molar mass of helium (4.00 g/mol).

Verified video answer for a similar problem:

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

Video duration:

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 is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the amount of gas in a given volume and conditions, which is essential for determining the mass of helium in the tire.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For helium, the molar mass is approximately 4.00 g/mol. Understanding molar mass is crucial for converting between the number of moles of gas and its mass, enabling us to find the total mass of helium in the tire once we calculate the number of moles using the Ideal Gas Law.

Gas Behavior at Different Conditions

Gases behave differently under varying conditions of pressure and temperature. At high pressures, gases can deviate from ideal behavior, but for many practical calculations, the Ideal Gas Law provides a good approximation. In this scenario, understanding how helium behaves at 7.80 atm and 25 °C is important for accurately determining its mass in the tire, as it influences the calculations derived from the Ideal Gas Law.

Recommended video:

Guided course

02:13

Ideal Gas Conditions Example

Related Practice

Textbook Question

The reaction of sodium peroxide 1Na2O22 with CO2 is used in space vehicles to remove CO2 from the air and generate O2 for breathing:2 Na2O21s2 + 2 CO21g2¡2 Na2CO31s2 + O21g2(a) Assuming that air is breathed at an average rate of 4.50 L/min (25 °C; 735 mm Hg) and that the concentration of CO2 in expelled air is 3.4% by volume, how many grams of CO2 are produced in 24 h?

Textbook Question

Titanium(III) chloride, a substance used in catalysts for preparing polyethylene, is made by high-temperature reaction of TiCl₄ vapor with H₂: 2 TiCl₄(g) + H₂(g) → 2 TiCl₃(s) + 2 HCl(g) (a) How many grams of TiCl₄ are needed for complete reaction with 155 L of H₂ at 435 °C and 795 mm Hg pressure?

Textbook Question

Titanium(III) chloride, a substance used in catalysts for preparing polyethylene, is made by high-temperature reaction of TiCl₄ vapor with H₂: 2 TiCl₄(g) + H₂(g) → 2 TiCl₃(s) + 2 HCl(g) (b) How many liters of HCl gas at STP will result from the reaction described in part (a)?

Textbook Question

Assume that you have 1.00 g of nitroglycerin in a 500.0-mL steel container at 20.0 °C and 1.00 atm pressure. An explosion occurs, raising the temperature of the container and its contents to 425 °C. The balanced equation is 4 C3H5N3O91l2¡ 12 CO21g2 + 10 H2O1g2 + 6 N21g2 + O21g2 (c) What is the pressure in atmospheres inside the container after the explosion according to the ideal gas law?