Question

A gas sample that has a mass of 0.993 g occupies 0.570 L. Given that the temperature is 281 K and the pressure is 1.44 atm, what is the molar mass of the gas?

Short answer

The molar mass of the gas is approximately 27.9 g/mol.

Step-by-step solution

- Recall the Ideal Gas Law

To find the molar mass of the gas, use the Ideal Gas Law: \[ PV = nRT \] where \(P\) is the pressure (1.44 atm), \(V\) is the volume (0.570 L), \(n\) is the number of moles, \(R\) is the ideal gas constant (0.0821 L·atm/(K·mol)), and \(T\) is the temperature (281 K).

- Solve for the number of moles

Rearrange the Ideal Gas Law to solve for the number of moles \(n\): \[ n = \frac{PV}{RT} \] Plug in the given values: \[ n = \frac{1.44 \text{ atm} \times 0.570 \text{ L}}{0.0821 \text{ L·atm/(K·mol)} \times 281 \text{ K}} \] Calculate \(n\): \[ n = \frac{0.8208}{23.0701} \approx 0.0356 \text{ mol} \]

- Find the molar mass

Use the relationship between mass, moles, and molar mass: \[ \text{Molar Mass} = \frac{ \text{Mass} }{ n } \] Substitute the known values for mass (0.993 g) and moles (0.0356 mol): \[ \text{Molar Mass} = \frac{0.993 \text{ g}}{0.0356 \text{ mol}} \] Calculate the molar mass: \[ \text{Molar Mass} \approx 27.9 \text{ g/mol} \]

Key concepts

Molar Mass Calculation

To determine the molar mass of a gas, we need to follow a few simple steps. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In the context of gases, this calculation can be simplified using the Ideal Gas Law.
First, use the Ideal Gas Law to find the number of moles of the gas. Then, divide the mass of the gas by the number of moles to get the molar mass.
For example, if you have a gas with a mass of 0.993 g that occupies 0.570 L, under a temperature of 281 K and a pressure of 1.44 atm, you would first calculate the number of moles using the Ideal Gas Law. Finally, you divide the mass by the number of moles to find the molar mass, which in this case is approximately 27.9 g/mol.

Gas Laws

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. The most commonly used gas law in these calculations is the Ideal Gas Law:

, where:
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They allow us to relate all these factors to each other. For instance, if we know the amount of gas in moles (n), the pressure (P), the volume (V), and the temperature (T), we can calculate the Ideal Gas Constant (R).
In our example, given the values of pressure (1.44 atm), volume (0.570 L), and temperature (281 K), we used the Ideal Gas Law to solve for the number of moles: Then we used the results to find the molar mass of the gas.

Chemical Stoichiometry

Chemical stoichiometry involves the calculation of the reactants and products in chemical reactions. It helps us understand the proportional relationships between different substances. For gases, stoichiometry can involve calculations like finding the number of moles from given masses and using gas volumes to find quantities.
This concept was applied in our example where we calculated the number of moles of the gas using the Ideal Gas Law, and then found the molar mass from this information. Knowing how to manipulate these quantities using stoichiometry is crucial for accurately solving problems in chemistry.
Always remember that accurate measurements and correct units are key in ensuring precise stoichiometry calculations.