Which sample contains more molecules: 2.0 L of Cl₂ at STP or 3.0 L of CH₄ at 300 K and 1150 mmHg? Which sample weighs more?

Verified step by step guidance

1. Determine the number of molecules in each sample using the ideal gas law. Start with the sample of Cl₂ at STP. At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L. Use the relationship: \( \text{moles of Cl}_2 = \frac{\text{volume of Cl}_2}{22.4 \text{ L/mol}} \). Then, calculate the number of molecules by multiplying the moles by Avogadro's number \( (6.022 \times 10^{23} \text{ molecules/mol}) \).
2. For the CH₄ sample, use the ideal gas law \( PV = nRT \) to calculate the number of moles. Rearrange the equation to solve for \( n \): \( n = \frac{PV}{RT} \). Convert the pressure from mmHg to atm using the conversion factor \( 1 \text{ atm} = 760 \text{ mmHg} \). Use \( R = 0.0821 \text{ L·atm/(mol·K)} \) and substitute the given values for pressure, volume, and temperature to find \( n \). Then, calculate the number of molecules by multiplying \( n \) by Avogadro's number.
3. Compare the number of molecules in the Cl₂ sample and the CH₄ sample to determine which contains more molecules.
4. To determine which sample weighs more, calculate the mass of each sample. For Cl₂, use the molar mass of Cl₂ (\( 70.90 \text{ g/mol} \)) and multiply it by the number of moles of Cl₂ calculated earlier. For CH₄, use the molar mass of CH₄ (\( 16.04 \text{ g/mol} \)) and multiply it by the number of moles of CH₄ calculated earlier.
5. Compare the masses of the Cl₂ sample and the CH₄ sample to determine which weighs more.

Key Concepts

Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle allows us to compare the number of molecules in different gas samples by considering their volumes under standard conditions, such as STP (Standard Temperature and Pressure).

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. This law can be used to calculate the number of moles of CH₄ at the given conditions (300 K and 1150 mmHg) to determine how many molecules are present in that sample.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To compare the weights of the two gas samples, we can calculate the mass of each gas using their respective molar masses (Cl₂ = 70.9 g/mol and CH₄ = 16.04 g/mol) and the number of moles derived from the Ideal Gas Law.