The enthalpy of combustion of methane,graphite and dihydrogen at $298 \, K$ are $-890.3 \, kJ \, mol^{-1}$,$-393.5 \, kJ \, mol^{-1}$ and $-285.8 \, kJ \, mol^{-1}$ respectively. The enthalpy of formation of $CH_{4(g)}$ will be:
$(i) -74.8 \, kJ \, mol^{-1}$
$(ii) -52.27 \, kJ \, mol^{-1}$
$(iii) +74.8 \, kJ \, mol^{-1}$
$(iv) +52.26 \, kJ \, mol^{-1}$
$(i) -74.8 \, kJ \, mol^{-1}$
$(ii) -52.27 \, kJ \, mol^{-1}$
$(iii) +74.8 \, kJ \, mol^{-1}$
$(iv) +52.26 \, kJ \, mol^{-1}$
(A) The combustion reactions are:
$(i) CH_{4(g)} + 2O_{2(g)} \longrightarrow CO_{2(g)} + 2H_{2}O_{(l)}; \Delta_cH = -890.3 \, kJ \, mol^{-1}$
$(ii) C_{(s)} + O_{2(g)} \longrightarrow CO_{2(g)}; \Delta_cH = -393.5 \, kJ \, mol^{-1}$
$(iii) H_{2(g)} + \frac{1}{2}O_{2(g)} \longrightarrow H_{2}O_{(l)}; \Delta_cH = -285.8 \, kJ \, mol^{-1}$
The formation reaction of $CH_{4(g)}$ is:
$C_{(s)} + 2H_{2(g)} \longrightarrow CH_{4(g)}$
Using Hess's Law:
$\Delta_fH_{CH_4} = \Delta_cH_{C(s)} + 2(\Delta_cH_{H_2(g)}) - \Delta_cH_{CH_4(g)}$
$\Delta_fH_{CH_4} = [-393.5 + 2(-285.8) - (-890.3)] \, kJ \, mol^{-1}$
$\Delta_fH_{CH_4} = [-393.5 - 571.6 + 890.3] \, kJ \, mol^{-1}$
$\Delta_fH_{CH_4} = -74.8 \, kJ \, mol^{-1}$
Thus,the enthalpy of formation is $-74.8 \, kJ \, mol^{-1}$,which corresponds to option $(i)$.
$(i) CH_{4(g)} + 2O_{2(g)} \longrightarrow CO_{2(g)} + 2H_{2}O_{(l)}; \Delta_cH = -890.3 \, kJ \, mol^{-1}$
$(ii) C_{(s)} + O_{2(g)} \longrightarrow CO_{2(g)}; \Delta_cH = -393.5 \, kJ \, mol^{-1}$
$(iii) H_{2(g)} + \frac{1}{2}O_{2(g)} \longrightarrow H_{2}O_{(l)}; \Delta_cH = -285.8 \, kJ \, mol^{-1}$
The formation reaction of $CH_{4(g)}$ is:
$C_{(s)} + 2H_{2(g)} \longrightarrow CH_{4(g)}$
Using Hess's Law:
$\Delta_fH_{CH_4} = \Delta_cH_{C(s)} + 2(\Delta_cH_{H_2(g)}) - \Delta_cH_{CH_4(g)}$
$\Delta_fH_{CH_4} = [-393.5 + 2(-285.8) - (-890.3)] \, kJ \, mol^{-1}$
$\Delta_fH_{CH_4} = [-393.5 - 571.6 + 890.3] \, kJ \, mol^{-1}$
$\Delta_fH_{CH_4} = -74.8 \, kJ \, mol^{-1}$
Thus,the enthalpy of formation is $-74.8 \, kJ \, mol^{-1}$,which corresponds to option $(i)$.
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Similar Questions
At $298 \ K$, the enthalpy change (in $kJ$) for the reaction given below is: $CH_{4(g)} + O_{2(g)} \rightarrow C_{(s)} + 2H_2O_{(l)}$
Given:
$1) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \rightarrow H_2O_{(l)} ; \Delta H^{\ominus} = -286 \ kJ$
$2) \ C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} ; \Delta H^{\ominus} = -394 \ kJ$
$3) \ CH_{4(g)} + 2O_{2(g)} \rightarrow CO_{2(g)} + 2H_2O_{(l)} ; \Delta H^{\ominus} = -890 \ kJ$
Given:
$1) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \rightarrow H_2O_{(l)} ; \Delta H^{\ominus} = -286 \ kJ$
$2) \ C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} ; \Delta H^{\ominus} = -394 \ kJ$
$3) \ CH_{4(g)} + 2O_{2(g)} \rightarrow CO_{2(g)} + 2H_2O_{(l)} ; \Delta H^{\ominus} = -890 \ kJ$
Find the value of $Q$ from the following equations:
$(i)$ $C_{(s)} + O_{2_{(g)}} \longrightarrow CO_{2_{(g)}}$ $\Delta H = Q \ kJ$
$(ii)$ $C_{(s)} + \frac{1}{2} O_{2_{(g)}} \longrightarrow CO_{(g)}$ $\Delta H = -x \ kJ$
$(iii)$ $CO_{(g)} + \frac{1}{2} O_{2_{(g)}} \longrightarrow CO_{2_{(g)}}$ $\Delta H = -y \ kJ$
$(i)$ $C_{(s)} + O_{2_{(g)}} \longrightarrow CO_{2_{(g)}}$ $\Delta H = Q \ kJ$
$(ii)$ $C_{(s)} + \frac{1}{2} O_{2_{(g)}} \longrightarrow CO_{(g)}$ $\Delta H = -x \ kJ$
$(iii)$ $CO_{(g)} + \frac{1}{2} O_{2_{(g)}} \longrightarrow CO_{2_{(g)}}$ $\Delta H = -y \ kJ$
Find the value of $x$ in $\text{kJ}$ using the following equations:
$H_2O_{(g)} + C_{(s)} \to CO_{(g)} + H_{2(g)} : \Delta H = 131 \ \text{kJ}$
$CO_{(g)} + \frac{1}{2} O_{2(g)} \to CO_{2(g)} : \Delta H = -282 \ \text{kJ}$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \to H_2O_{(g)} : \Delta H = -242 \ \text{kJ}$
$C_{(s)} + O_{2(g)} \to CO_{2(g)} : \Delta H = x \ \text{kJ}$
$H_2O_{(g)} + C_{(s)} \to CO_{(g)} + H_{2(g)} : \Delta H = 131 \ \text{kJ}$
$CO_{(g)} + \frac{1}{2} O_{2(g)} \to CO_{2(g)} : \Delta H = -282 \ \text{kJ}$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \to H_2O_{(g)} : \Delta H = -242 \ \text{kJ}$
$C_{(s)} + O_{2(g)} \to CO_{2(g)} : \Delta H = x \ \text{kJ}$
Medium
View SolutionGiven the following thermochemical equations:
$(1) \ H_2O_{(g)} + C_{(s)} \to CO_{(g)} + H_{2(g)} ; \Delta H_1 = 100 \ kJ$
$(2) \ CO_{(g)} + \frac{1}{2}O_{2_{(g)}} \to CO_{2_{(g)}} ; \Delta H_2 = -300 \ kJ$
$(3) \ H_{2(g)} + \frac{1}{2}O_{2_{(g)}} \to H_2O_{(g)} ; \Delta H_3 = -250 \ kJ$
Calculate the value of $x$ for the reaction:
$(4) \ C_{(s)} + O_{2_{(g)}} \to CO_{2_{(g)}} ; \Delta H_4 = -x \ kJ$
$(1) \ H_2O_{(g)} + C_{(s)} \to CO_{(g)} + H_{2(g)} ; \Delta H_1 = 100 \ kJ$
$(2) \ CO_{(g)} + \frac{1}{2}O_{2_{(g)}} \to CO_{2_{(g)}} ; \Delta H_2 = -300 \ kJ$
$(3) \ H_{2(g)} + \frac{1}{2}O_{2_{(g)}} \to H_2O_{(g)} ; \Delta H_3 = -250 \ kJ$
Calculate the value of $x$ for the reaction:
$(4) \ C_{(s)} + O_{2_{(g)}} \to CO_{2_{(g)}} ; \Delta H_4 = -x \ kJ$
Medium
View SolutionState Hess's Law of Constant Heat Summation.
Easy
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