Natural gas is a mixture of hydrocarbons, primarily methane 1CH42 and ethane 1C2H62. A typical mixture might have Xmethane = 0.915 and Xethane = 0.085. Let's assume that we have a 15.50 g sample of natural gas in a volume of 15.00 L at a temperature of 20.00 °C. (a) How many total moles of gas are in the sample?

검증된 단계별 안내

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary for calculations involving gases, which typically use the Kelvin scale.

Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L atm K^{-1} mol^{-1}), and T is the temperature in Kelvin. Rearrange the equation to solve for n (the number of moles): n = \(\frac{PV}{RT}\).

Assume standard atmospheric pressure (1 atm) for the pressure P, since it is not specified in the problem.

Substitute the values for P, V, R, and T into the rearranged ideal gas law equation to calculate the number of moles of gas in the sample.

This calculation will give you the total moles of gas in the sample, which includes both methane and ethane.

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.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For hydrocarbons like methane (CH4) and ethane (C2H6), the molar masses are approximately 16.04 g/mol and 30.07 g/mol, respectively. Understanding molar mass is essential for converting between grams and moles, which is necessary for calculating the total moles of gas in a sample.

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 number of moles of gas present in a given volume and conditions, which is crucial for solving the problem.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles in the mixture. In the context of natural gas, knowing the mole fractions of methane and ethane helps in determining their contributions to the total moles of gas. This concept is important for understanding the composition of the gas sample and performing calculations related to it.