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A 4.05 g sample of an unknown gas at 69 C and 1.00 atm is stored in a 1.75 L flask. What is the density of the gas?

Answer

The density of the gas can be calculated using the Ideal Gas Law. The Ideal Gas Law states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is temperature. The density of the gas is equal to the mass of the gas divided by the volume of the gas.

Calculations

The first step is to calculate the number of moles of the gas. This can be done by using the Ideal Gas Law equation and solving for n. The pressure is 1.00 atm, the volume is 1.75 L, the temperature is 69 C, and the ideal gas constant is 0.0821 L atm mol-1K-1. Plugging these values into the equation, the number of moles of the gas is 0.0332 moles. The next step is to calculate the mass of the gas. This can be done by multiplying the number of moles of the gas by the molar mass of the gas, which is 4.05 g/mole. The mass of the gas is then 0.134 g. The last step is to calculate the density of the gas. This can be done by dividing the mass of the gas by the volume of the gas. The density of the gas is 0.077 g/L.

Conclusion

The density of the gas can be calculated by using the Ideal Gas Law equation and solving for the number of moles of the gas, then multiplying the number of moles by the molar mass of the gas to get the mass of the gas, and finally dividing the mass of the gas by the volume of the gas to get the density of the gas. The density of the gas in this case is 0.077 g/L.

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