In Section 2.1 it was pointed out that mass and energy are alternate aspects of a single entity called mass-energy. The relationship between these two physical quantities is Einstein's famous equation, \(E=m c^{2},\) where \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light. In a combustion experiment, it was found that \(12.096 \mathrm{~g}\) of hydrogen molecules combined with \(96.000 \mathrm{~g}\) of oxygen molecules to form water and released \(1.715 \times 10^{3} \mathrm{~kJ}\) of heat. Calculate the corresponding mass change in this process and comment on whether the law of conservation of mass holds for ordinary chemical processes. (Hint: The Einstein equation can be used to calculate the change in mass as a result of the change in energy. \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} / \mathrm{s}^{2}\) and \(\left.c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s} .\right)\)

Step by step solution

01

Understanding the principle

Firstly, it's essential to understand Einstein's mass-energy equivalence principle which states that mass can be converted into energy and vice-versa. This can be calculated using the equation \(E=mc^{2}\) where E is the energy, m is the mass, and c is the speed of light \(3.00 \times 10^{8} m/s\). One Joule (J) of energy is equivalent to \(1 kg*m^{2}/s^{2}\).

02

Convert energy from kJ to J

The energy released is given as \(1.715 \times 10^{3} kJ\). We can convert this to joules (J) for easier calculation as \(1 kJ = 1000 J\). Therefore, the energy in joules will be \(1.715 \times 10^{3} kJ * 1000 = 1.715 \times 10^{6} J\).

03

Calculate the change in mass

We now use Einstein's energy-mass equivalence formula, \(E = mc^{2}\), to find the change in mass. Making mass the subject of the formula, we have \(m = E / c^{2}\). Substituting the values of E and c into the formula, we get \(m = 1.715 \times 10^{6} J / (3.00 \times 10^{8} m/s)^{2} = 1.905 \times 10^{-11} kg\).

04

Convert mass from kg to g

The standard SI unit for mass is kg, but the masses given in the problem are in g. Hence, the calculated mass difference should be converted into grams as \(1kg = 1000g\). So the change in mass is \(1.905 \times 10^{-11} kg * 1000 = 1.905 \times 10^{-8} g\).

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