Question

The volume occupied by \(7 \mathrm{~g}\) of nitrogen gas at \(\mathrm{STP}\) is

Short answer

Answer: The volume occupied by 7 grams of nitrogen gas at STP is 5.6 liters.

Step-by-step solution

Find molar mass of nitrogen gas

To find the molar mass of nitrogen gas, we need to know the molecular formula of nitrogen gas is \(\mathrm{N_{2}}\). From the periodic table, we find that the atomic mass of nitrogen is 14.0067 amu, so the molar mass of nitrogen gas is: Molar mass of \(\mathrm{N_{2}} = 2 \times 14.0067 \text{ amu} = 28.0134 \mathrm{~g/mol}\)

Convert mass into moles

Next, convert the given mass of nitrogen gas (7 grams) into moles using the molar mass from Step 1: Moles of \(\mathrm{N_{2}} = \dfrac{\text{mass of nitrogen gas}}{\text{molar mass of }\mathrm{N_{2}}} = \dfrac{7 \mathrm{~ g}}{28.0134 \mathrm{~g/mol}} = 0.25 \mathrm{~ moles}\)

Use the molar volume of a gas at STP

At standard temperature and pressure (STP), the molar volume of a gas is 22.4 liters per mole. This means that one mole of any gas occupies 22.4 liters of volume at STP.

Calculate the volume occupied by the gas

Finally, use the moles of nitrogen gas and the molar volume at STP to calculate the volume occupied by the gas: Volume occupied by \(\mathrm{N_{2}} = \text{moles of }\mathrm{N_{2}} \times \text{molar volume at STP} = 0.25 \mathrm{~ moles} \times 22.4 \mathrm{~ L/mol} = 5.6 \mathrm{~ L}\) Therefore, the volume occupied by 7 grams of nitrogen gas at STP is 5.6 liters.