To find the mass of nitrogen ([tex]\(N_2\)[/tex]) in grams when given the number of moles, you can use the formula:
[tex]\[ \text{Mass} = \text{Molar Mass} \times \text{Number of Moles} \][/tex]
Here are the steps:
1. Identify the molar mass of [tex]\(N_2\)[/tex]:
The molar mass of nitrogen gas ([tex]\(N_2\)[/tex]) is given as [tex]\(28.02 \, \text{g/mol}\)[/tex].
2. Identify the number of moles of [tex]\(N_2\)[/tex]:
The number of moles given is [tex]\(4.60 \, \text{mol}\)[/tex].
3. Substitute the values into the formula:
[tex]\[
\text{Mass} = 28.02 \, \text{g/mol} \times 4.60 \, \text{mol}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Mass} = 128.892 \, \text{g}
\][/tex]
Therefore, the mass of [tex]\(4.60 \, \text{mol}\)[/tex] of [tex]\(N_2\)[/tex] is approximately [tex]\(129 \, \text{grams}\)[/tex] (rounded to three significant figures). So the correct answer is:
129 grams
