Question

consider the following thermochemical equation:
2 nh₃(g) → n₂(g) + 3 h₂(g)
δh = +91.8 kj/mol
how much energy is required to decompose 45.0 g nh₃(g)?
4131 kj
2066 kj
242 kj
121 kj

Explanation:

Step1: Calculate the molar mass of \(NH_3\)

The molar mass of \(N = 14.01\ g/mol\) and \(H=1.008\ g/mol\). For \(NH_3\), \(M = 14.01+(3\times1.008)=17.034\ g/mol\)

Step2: Calculate the number of moles of \(NH_3\)

Using the formula \(n=\frac{m}{M}\), where \(m = 45.0\ g\) and \(M = 17.034\ g/mol\). So \(n=\frac{45.0}{17.034}\approx2.64\ mol\)

Step3: Use the thermochemical equation to find the energy

From \(2NH_3(g)\to N_2(g)+3H_2(g)\), \(\Delta H = + 91.8\ kJ/mol\) (for \(2\) moles of \(NH_3\)).
For \(2.64\) moles of \(NH_3\), the energy \(E\) is calculated as follows:
If \(2\) moles of \(NH_3\) require \(91.8\ kJ\), then for \(n = 2.64\) moles
\(E=\frac{91.8}{2}\times2.64\)
\(E = 45.9\times2.64=121\ kJ\)

Answer:

121 kJ