A sample of N₂O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?

검증된 단계별 안내

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

Express the number of moles \( n \) in terms of mass and molar mass: \( n = \frac{m}{M} \), where \( m \) is mass and \( M \) is molar mass.

Substitute \( n = \frac{m}{M} \) into the ideal gas law to get \( PV = \frac{m}{M}RT \).

Rearrange the equation to solve for pressure \( P \): \( P = \frac{mRT}{MV} \).

Use the density formula \( \text{density} = \frac{m}{V} \) to substitute \( m/V \) with density in the pressure equation: \( P = \frac{\text{density} \times RT}{M} \).

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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 one variable if the others are known, making it essential for solving gas-related problems.

Density of Gases

The density of a gas is defined as its mass per unit volume, typically expressed in grams per liter (g/L). For gases, density can be influenced by temperature and pressure, and it can be calculated using the formula density = mass/volume. Understanding how to manipulate this relationship is crucial for converting density into other gas properties, such as pressure.

Conversion of Units

In chemistry, it is often necessary to convert between different units of measurement, such as from grams to moles or from liters to milliliters. For this problem, converting pressure from atmospheres or pascals to mmHg is essential, as different contexts may require different units. Familiarity with conversion factors and the relationships between units is vital for accurate calculations.

A sample of N2O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?