Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12°C and 743 torr.

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).
2. Convert the pressure from torr to atm using the conversion factor: \( 1 \text{ atm} = 760 \text{ torr} \).
3. Use the ideal gas law equation in the form \( PV = nRT \) to solve for the molar mass \( M \). Rearrange it to \( M = \frac{dRT}{P} \), where \( d \) is the density, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), \( T \) is the temperature in Kelvin, and \( P \) is the pressure in atm.
4. Substitute the values for density, \( R \), temperature in Kelvin, and pressure in atm into the rearranged ideal gas law equation.
5. Calculate the molar mass using the substituted values.

Key Concepts

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 understanding how gases behave under different conditions and is used to derive relationships between density, molar mass, and other properties of gases.

Density of Gases

Density is defined as mass per unit volume. For gases, density can be influenced by temperature and pressure. The density of a gas can be used in conjunction with the Ideal Gas Law to calculate molar mass, as it provides a direct relationship between the mass of the gas and its volume under specific conditions.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of a vapor using its density, temperature, and pressure, one can rearrange the Ideal Gas Law to find the molar mass in terms of these variables, allowing for the determination of the substance's identity.