A 22.0 gram sample of an unknown gas occupies 11.2 liters at standard temperature and pressure. Which of the following could be the identity of the gas? (A) \(\mathrm{CO}_{2}\) (B) \(\mathrm{SO}_{3}\) (C) \(\mathrm{O}_{2}\) (D) He

Short Answer

Expert verified
The identity of the gas could be CO2.

Step by step solution

01

Calculate the moles of the gas

Using Avogadro's law, that a gas at STP occupies a volume of 22.4 liters per mole, calculate the moles of the gas. In this case, \(11.2 \, \mathrm{liters} \, \times \, \frac{1 \, \mathrm{mole}}{22.4 \, \mathrm{liters}} = 0.5 \, \mathrm{mole}\) of gas.
02

Calculate the molar mass of the gas

Molar mass is calculated by dividing the mass of the gas by the moles of the gas. Here, the molar mass is \( \frac{22.0 \, \mathrm{g}}{0.5 \, \mathrm{mole}} = 44.0 \, \mathrm{g/mole}\).
03

Compare the calculated molar mass with the given gases

Looking at the molar masses of the given gases: CO2 = 44.0 g/mole, SO3 = 80.1 g/mole, O2 = 32.0 g/mole, He = 4.0 g/mole. The unknown gas could be CO2 because its molar mass matches with the calculated molar mass.

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