What are the molecular weights of the gases with the following densities: (b) 1.053 g/L at 25 °C and 752 mm Hg

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Identify the formula to use: The molecular weight (molar mass) of a gas can be determined using the ideal gas law equation rearranged to solve for molar mass: \( M = \frac{dRT}{P} \), where \( M \) is the molar mass, \( d \) is the density, \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( P \) is the pressure.

Convert the temperature from Celsius to Kelvin: Use the formula \( T(K) = T(°C) + 273.15 \) to convert 25 °C to Kelvin.

Convert the pressure from mm Hg to atm: Use the conversion factor \( 1 \text{ atm} = 760 \text{ mm Hg} \) to convert 752 mm Hg to atm.

Substitute the known values into the formula: Use the density \( d = 1.053 \text{ g/L} \), the converted temperature in Kelvin, the converted pressure in atm, and the ideal gas constant \( R = 0.0821 \text{ L atm/mol K} \).

Calculate the molar mass: Perform the calculation using the substituted values to find the molar mass of the gas.

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주요 개념

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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the molecular weight of a gas when its density, temperature, and pressure are known. By rearranging the equation, one can derive the molecular weight from the density and the conditions of the gas.

Density of Gases

Density is defined as mass per unit volume. For gases, density can be expressed in grams per liter (g/L). Understanding how to convert between density, mass, and volume is crucial for determining the molecular weight of a gas, as it allows for the calculation of the mass of a specific volume of gas under given conditions.

Molecular Weight Calculation

Molecular weight, or molar mass, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molecular weight of a gas from its density, one can use the formula: Molecular Weight = Density × (RT/P), where R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure in atmospheres. This calculation is fundamental in stoichiometry and gas law applications.