Question

Hydrogen gives off 120. J/g of energy when burned in oxygen, and methane gives off 50. J/g under the same circumstances. If a mixture of 5.0 g hydrogen and 10. g methane is burned, and the heat released is transferred to 50.0 g water at 25.0⁰C, what final temperature will be reached by the water?

Short answer

The final temperature reached by the water will be 30.26⁰C

Step-by-step solution

Step 1:Determine the heat released

Hydrogen gives off 120. J/g of energy when burned in oxygen, and methane gives off 50. J/g under the same circumstances.

If a mixture of 5 g of hydrogen and 10g of methane burned then the amount of heat released will be

$$\begin{gathered} =\left(120\times 5+50\times 10\right)J \\ =1100J \end{gathered}$$

Determine the final temperature

From the given information we can write

Heat gain by water=Heat loss by Hydrogen+ Heat loss by Methane

Let us assume,

$\begin{array}{rcl}m& =& massoftheelement\\ C_P& =& Heatcapacity\\ ∆T& =& Changeintemperature\\ T_f& =& Finaltemperature\\ Q& =& Amountofheat\end{array}$

Given

Mass of water= 50.0 g

It is known that Specific heat capacity of water =4.18 J ⁰C^-1 g^-1

$\begin{array}{rcl}50.0g{H}_{2}O\times 4.18\frac{J}{g°C}\times \left(T_f-25\right)°C& =& 1100J\\ \left(T_f-25\right)°C& =& \frac{1100}{50\times 4.18}\\ \left(T_f-25\right)°C& =& 5.26°C\\ T_f& =& 30.26°C\end{array}$

The final temperature reached by the water will be 30.26⁰C