ANSWER
The heat of formation of propane is -195KJ
EXPLANATION
Given that;
[tex]\begin{gathered} \text{ H}_{2(g)}\text{ + }\frac{1}{2}O_{2(g)}\text{ }\rightarrow\text{ H}_2O;\text{ }\Delta H\text{ = -395KJ ------- equation }\alpha \\ \\ \text{ C}_{(s)}\text{ + O}_{2(g)}\rightarrow\text{ CO}_{(2)(g)}\text{ ; }\Delta H\text{ = -280KJ ------- equation }\beta \\ \\ \text{ C}_3\text{ H}_8\text{ + 5O}_2\text{ }\rightarrow\text{ 3CO}_{2(g)}\text{ + 4H}_2O;\text{ }\Delta H\text{ = -2225KJ ------ equation }\gamma \end{gathered}[/tex]Follow the steps below to find the heat of formation of propane
Step 1; multiply equation alpha by 4
[tex]\begin{gathered} \text{ H}_{2(g)}\text{ + }\frac{1}{2}O_{2(g)}\text{ }\rightarrow\text{ H}_2O\text{ }\times\text{ 4} \\ \text{ 4H}_2\text{ + 4 }\times\frac{1}{2}O_2\text{ }\rightarrow\text{ 4H}_2O \\ \text{ 4H}_2\text{ + 2O}_2\text{ }\rightarrow\text{ 4H}_2O\text{ ---------- }\alpha1 \end{gathered}[/tex]Step 2; multiply equation beta by 3
[tex]\begin{gathered} \text{ C}_{(s)}\text{ + O}_{2(g)}\text{ }\rightarrow\text{ CO}_{2(g)}\text{ }\times\text{ 3} \\ \text{ 3C}_{(s)}\text{ + 3O}_{2(g)}\text{ }\rightarrow\text{ 3CO}_{2(g)}\text{ ----------}\beta1 \\ \text{ } \end{gathered}[/tex]Step 3; Reverse the equation gamma
[tex]\text{ 3CO}_{2(g)}\text{ + 4H}_2O_{(l)}\text{ }\rightarrow\text{ C}_3H_{8(g)}\text{ + 5O}_{2(g)}\text{ ------}\gamma1[/tex]Step 4; Add equation alpha1, beta1, and gamma1 together
[tex]\begin{gathered} \text{ 4H}_{2(g)}\text{ + 2O}_{2(g)}_\text{ + 3O}_{2(g)}+\text{ 3C}_{(s)}\text{ + 3CO}_{2(g)}\text{ + 4H}_2O(l)\text{ }\rightarrow\text{ 4H}_2O(l)\text{ + 3CO}_{2(g)}\text{ + 5O}_{2(g)}\text{ + C}_3H_{8(g)} \\ \text{ 4H}_{2(g)}\text{ + 5O}_{2(g)}\text{ + 3C}_{(s)}\text{ + 3CO}_{2(g)}\text{ + 4H}_2O(l)\text{ }\rightarrow\text{ 4H}_2O(l)\text{ + 3CO}_{2(g)}\text{ + 5O}_{2(g)}\text{ + C}_3H_{8(g)} \\ \text{ 4H}_{2(g)}+\cancel{5O_2}+\cancel{3CO_2}+\cancel{4H_2}O\text{ + 3C}\rightarrow\cancel{4H_2}O+\cancel{3CO_2}+\cancel{5O_2}\text{ + C}_3H_8 \\ \text{ 4H}_{2(g)}\text{ + 3C}_{(s)}\text{ }\rightarrow\text{ C}_3H_{8(g)} \\ \end{gathered}[/tex]Step 5 ; Evaluate the heat of formation of propane
[tex]\begin{gathered} \text{ 4H}_{2(g)}\text{ + 3C}_{(s)}\text{ }\rightarrow\text{ C}_3H_8 \\ \Delta H_f\text{ =\lparen4 }\times\text{ -395\rparen + \lparen-280}\times3)\text{ + 2225} \\ \text{ }\Delta H_f\text{ =-1580 - 840 + 2225} \\ \text{ }\Delta H_f\text{ = -2420 + 2225} \\ \text{ }\Delta H_f\text{ = -195KJ} \end{gathered}[/tex]Therefore, the heat of formation of propane is -195KJ
