If 2.00 g of N2 gas has a volume of 0.40 L and a pressure of 6.0 atm, what is its Kelvin temperature?

검증된 단계별 안내

Identify the known values: mass of N2 (m) = 2.00 g, volume (V) = 0.40 L, pressure (P) = 6.0 atm.

Use the ideal gas law equation, which is PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and T is the temperature in Kelvin.

Calculate the number of moles (n) of N2. First, find the molar mass of N2 (28.02 g/mol). Then, use n = \(\frac{m}{Molar\ mass}\) to find the moles of N2.

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

Plug in the values into the rearranged equation to find the temperature in Kelvin.

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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 the temperature in Kelvin. This law allows us to calculate one variable if the others are known, making it essential for solving gas-related problems.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For nitrogen gas (N2), the molar mass is approximately 28.02 g/mol, as it consists of two nitrogen atoms. Understanding molar mass is crucial for converting between grams and moles, which is necessary for applying the Ideal Gas Law in this question.

Temperature in Kelvin

Temperature in Kelvin is the absolute temperature scale used in scientific calculations, where 0 K represents absolute zero, the point at which molecular motion ceases. To convert Celsius to Kelvin, one adds 273.15. In gas law calculations, using Kelvin is essential because it ensures that temperature values are always positive, which is necessary for the mathematical relationships in the Ideal Gas Law.