Chapter 26, Problem 66GP

To determine

The mass of the elements decreases in given reaction and the percentage of the total original mass of the system.

Answer to Problem 66GP

The mass of the elements decreases in given reaction: $\text{5}\text{.38}{\text{×10}}^{\text{-12}}\text{kg}$

The percentage of the total original mass of the system: $1.49\times {10}^{-8}\%$

Explanation of Solution

Given:

Energy, $\text{E}\text{=}\text{484}\text{kJ}\text{=}\text{484}{\text{×10}}^{\text{3}}\text{J}$

Formula used:

It is known that

  $\text{Δm=}\frac{\text{ΔE}}{{\text{c}}^{\text{2}}}$

Where,

  $m$ is mass.

  $E$ is Energy

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

Calculation:

First calculate the loss in mass from $\text{Δm=}\frac{\text{ΔE}}{{\text{c}}^{\text{2}}}$

  $\text{Δm}\text{=}\frac{\text{484}{\text{×10}}^{\text{3}}\text{J}}{\text{3}\text{.00}\text{×}{\text{10}}^{\text{8}}\text{m/s}}\text{=5}\text{.38}{\text{×10}}^{\text{-12}}\text{kg}$

It is known that one mole of hydrogen weighs $\text{1}\text{g}\text{=}\text{0}\text{.001}\text{kg}$ and one mole of oxygen weighs $\text{16}\text{g}\text{=}\text{0}\text{.016}\text{kg}$

Two moles of water have a mass of $\text{36}{\text{.0×10}}^{\text{-3}}\text{kg}$ . So, the percentage of mass loss is

  $\frac{\text{5}\text{.38}{\text{×10}}^{\text{-12}}\text{kg}}{36.0\times {10}^{-3}\text{kg}}\text{=}1.49\times {10}^{-8}\%$