Question

consider the following decomposition reaction:
2nh₃(g) + 22.0 kcal → 3h₂(g) + n₂(g)
calculate the mass (in grams) of n₂ produced when 4.52 × 10⁴ kcal is consumed in this reaction. report your answer in scientific notation. be sure your answer has the correct number of significant figures.
g n₂

Explanation:

Step1: Find moles of \(N_2\) from kcal

The reaction is \(2NH_3(g)+22.0\ kcal
ightarrow3H_2(g)+N_2(g)\). So, 22.0 kcal produces 1 mole of \(N_2\).
Moles of \(N_2\) from \(4.52\times10^4\ kcal\): \(\frac{4.52\times10^4\ kcal}{22.0\ kcal/mol}=2.0545\times10^3\ mol\) (approx)

Step2: Calculate mass of \(N_2\)

Molar mass of \(N_2\) is \(2\times14.01 = 28.02\ g/mol\).
Mass = moles × molar mass = \(2.0545\times10^3\ mol\times28.02\ g/mol\)
\(= 2.0545\times28.02\times10^3\ g\)
\(= 57.567\times10^3\ g = 5.76\times10^4\ g\) (after significant figures, 3 sig figs from 4.52×10⁴ and 22.0)

Answer:

\(5.76\times10^4\)