Question

when 100. g of gaseous water decomposes 1337 kj of heat are used by the reaction. how much heat would be needed to decompose water and produce 17 g of oxygen gas?
\ce{h2o(g) -> \frac{1}{2}o2(g) + h2(g)}

Explanation:

Step1: Relate mass to moles of O₂

Molar mass of $\text{O}_2$ is $32\ \text{g/mol}$. Moles of $\text{O}_2$:
$$n_{\text{O}_2} = \frac{17\ \text{g}}{32\ \text{g/mol}}$$

Step2: Link reaction heat to O₂ moles

From the reaction, producing $\frac{1}{2}\ \text{mol O}_2$ uses $1337\ \text{kJ}$. Set up proportion:
$$\frac{x}{17\ \text{g}} = \frac{1337\ \text{kJ}}{16\ \text{g}}$$
(Note: 16 g is $\frac{1}{2} \times 32\ \text{g}$, the mass of $\frac{1}{2}$ mol O₂)

Step3: Calculate required heat

Solve for $x$:
$$x = \frac{17\ \text{g} \times 1337\ \text{kJ}}{16\ \text{g}}$$
$$x = 1423.5625\ \text{kJ}$$

Answer:

$1423.6\ \text{kJ}$ (rounded to 1 decimal place, or $1424\ \text{kJ}$ rounded to whole number)

Filled proportion for the given template:
$$\frac{1337}{16} = \frac{x}{17}$$
(16 comes from $\frac{1}{2} \times 32$, the molar mass of half a mole of O₂)