Question

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?

Accepted Answer

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: $$ 	ext{moles of Cl}_2 = \frac{	ext{volume of Cl}_2}{22.4 	ext{ L/mol}} . $$Then, calculate the number of molecules by multiplying the moles by Avogadro's number $$ (6.022 	imes 10^{23} 	ext{ molecules/mol}) . $$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 $$ 1 	ext{ atm} = 760 	ext{ mmHg} . $$Use $$ R = 0.0821 	ext{ L·atm/(mol·K)} $$ 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. Compare the number of molecules in the Cl₂ sample and the CH₄ sample to determine which contains more molecules. To determine which sample weighs more, calculate the mass of each sample. For Cl₂, use the molar mass of Cl₂ ($$ 70.90 	ext{ g/mol} ) $$and multiply it by the number of moles of Cl₂ calculated earlier. For CH₄, use the molar mass of CH₄ ($$ 16.04 	ext{ g/mol} ) $$and multiply it by the number of moles of CH₄ calculated earlier. Compare the masses of the Cl₂ sample and the CH₄ sample to determine which weighs more.

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?

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Key Concepts

Avogadro's Law

Ideal Gas Law

Molar Mass