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?

검증된 단계별 안내

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).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.