What is the temperature of 3.05 g of helium gas at a pressure of 1.70 atm and a volume of 14.1 L?

검증된 단계별 안내

Identify the ideal gas law equation: \( PV = nRT \).

Calculate the number of moles of helium gas using its molar mass: \( n = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of helium is approximately 4.00 g/mol.

Substitute the given values into the ideal gas law equation: \( P = 1.70 \text{ atm} \), \( V = 14.1 \text{ L} \), and the calculated \( n \). Use \( R = 0.0821 \text{ L atm/mol K} \) for the ideal gas constant.

Rearrange the ideal gas law equation to solve for temperature \( T \): \( T = \frac{PV}{nR} \).

Substitute the known values into the rearranged equation to find the temperature \( T \).

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주요 개념

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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 temperature of a gas when the other variables are known.

Molar Mass of Helium

Helium is a noble gas with a molar mass of approximately 4.00 g/mol. Understanding the molar mass is essential for converting the mass of helium (3.05 g) into moles, which is necessary for using the Ideal Gas Law. The number of moles can be calculated using the formula n = mass/molar mass.

Units of Measurement

In gas law calculations, it is crucial to use consistent units. Pressure should be in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K). To convert Celsius to Kelvin, add 273.15. Ensuring that all units are compatible is vital for accurate calculations and results.