# Given the following data, what is the enthalpy associated with the reaction? (i) 3H_2(g) + O_3(g) rarr 3H_2O(g); DeltaH_"rxn"=??

## $\left(i i\right)$ $2 {H}_{2} \left(g\right) + {O}_{2} \left(g\right) \rightarrow 2 {H}_{2} O \left(g\right)$; $\Delta {H}_{1} = - 483.6 \cdot k J \cdot m o {l}^{-} 1$ $\left(i i i\right)$ $3 {O}_{2} \left(g\right) \rightarrow 2 {O}_{3} \left(g\right)$; $\Delta {H}_{2} = 284. .6 \cdot k J \cdot m o {l}^{-} 1$

Jun 21, 2016

Approx. $- 100 \cdot k J \cdot m o {l}^{-} 1$

#### Explanation:

$\left(i\right)$ $3 {H}_{2} \left(g\right) + {O}_{3} \left(g\right) \rightarrow 3 {H}_{2} O \left(g\right)$; DeltaH_?=??

$\left(i i\right)$ $2 {H}_{2} \left(g\right) + {O}_{2} \left(g\right) \rightarrow 2 {H}_{2} O \left(g\right)$; $\Delta {H}_{1} = - 483.6 \cdot k J \cdot m o {l}^{-} 1$

$\left(i i i\right)$ $3 {O}_{2} \left(g\right) \rightarrow 2 {O}_{3} \left(g\right)$; $\Delta {H}_{2} = 284. .6 \cdot k J \cdot m o {l}^{-} 1$

Treating these algebraically:

$\frac{1}{2} \times \left(i i i\right) + \frac{3}{2} \times \left(i i\right)$ $=$

$3 {H}_{2} \left(g\right) + 3 {O}_{2} \left(g\right) \rightarrow 3 {H}_{2} O \left(g\right) + {O}_{3} \left(g\right)$ $=$ $\left(i\right)$ as required.

And thus DeltaH_?=3/2DeltaH_2+1/2DeltaH_1

$\left(\frac{3}{2} \left(284.6\right) + \frac{1}{2} \left(- 483.6\right)\right) \cdot k J \cdot m o {l}^{-} 1$ $=$ ???

All I have done here is treated each reaction algebraically. In effect, this is a problem with 2 linear equations and 2 unknowns. If I had to reverse the equations, I would have had to reverse the sign on $\Delta H$. Capisce?