Mass Calculation for \(N_2\) Gas

This question asks us to find the mass of a specific amount (0.5 mole) of nitrogen gas (\(N_2\)). To solve this, we need to understand the relationship between moles, molar mass, and mass.

Understanding Molar Mass

The molar mass of a substance is the mass of one mole of that substance, typically measured in grams per mole (g/mol).

• The atomic mass of Nitrogen (N) is approximately 14 g/mol.
• Since nitrogen gas exists as a diatomic molecule (\(N_2\)), its molar mass is calculated by multiplying the atomic mass of nitrogen by 2.

Calculation of molar mass for \(N_2\):

\(\text{Molar Mass of } N_2 = 2 \times (\text{Atomic Mass of N})\)

\(\text{Molar Mass of } N_2 = 2 \times 14 \text{ g/mol}\)

\(\text{Molar Mass of } N_2 = 28 \text{ g/mol}\)

Calculating Mass from Moles

The relationship between mass, moles, and molar mass is given by the formula:

\(\text{Mass} = \text{Moles} \times \text{Molar Mass}\)

We are given:

• Moles = 0.5 mol
• Molar Mass of \(N_2\) = 28 g/mol

Now, we can substitute these values into the formula:

\(\text{Mass of } N_2 = 0.5 \text{ mol} \times 28 \text{ g/mol}\)

\(\text{Mass of } N_2 = 14 \text{ g}\)

Conclusion

Therefore, the mass of 0.5 mole of \(N_2\) gas is 14 grams.