Question #8a2b4
1 Answer
Explanation:
The idea here is that you need to use Einstein's equation to convert the difference in mass between the helium-4 atom and the sum of the hydrogen-3 and hydrogen-1 atoms to energy.
color(blue)(E = m * c^2)" "E=m⋅c2 , where
The idea here is that the atomic mass of the helium-4 atom will be smaller than the sum of the atomic masses of the hydrogen-3 and hydrogen-1 atoms because some of that mass is converted to energy.
The sum of the hydrogen-3 and hydrogen-1 atoms will be
m_"total" = "3.016049 u" + "1.007825 u" = "4.023874 u"mtotal=3.016049 u+1.007825 u=4.023874 u
The difference between this value and the actual mass of the helium-4 atom, also called mass defect, will be
m_"diff" = "4.023874 u" - "4.002603 u" = "0.021271 u"mdiff=4.023874 u−4.002603 u=0.021271 u
Now, the unified atomic mass unit,
"1 u" = 1.660539 * 10^(-27)"kg"1 u=1.660539⋅10−27kg
Use this conversion factor to convert the mass defect from unified atomic mass units to kilograms
0.021271 color(red)(cancel(color(black)("u"))) * (1.660539 * 10^(-27)"kg")/(1color(red)(cancel(color(black)("u")))) = 3.532133 * 10^(-29)"kg"
Use Einstein's equation to calculate the energy released per atom of hydrogen-3 and hydrogen-1
E = 3.532133 * 10^(-29) * ("299,792,458")^2 overbrace("kg m"^2"s"^(-2))^(color(blue)("Joules"))
E = 3.174523* 10^(-12)"J"
Now, to get the energy released per gram of reactant, use Avogadro's number to first convert the energy from Joules per atom to Joules per mole
3.174523 * 10^(12)"J"/color(red)(cancel(color(black)("atom"))) * (6.022 * 10^(23)color(red)(cancel(color(black)("atoms"))))/"1 mole" = 1.911698 * 10^12"J/mol"
Now, the total atomic mass of the reactants is equal to
"1 u " = " 1 g/mol"
to get a total molar mass of the reactants of
1.911698 * 10^(12)"J"/color(red)(cancel(color(black)("mol"))) * (1color(red)(cancel(color(black)("mol"))))/"4.023874 g" = color(green)(4.750089 * 10^(11)"J/g")
The answer is rounded to seven sig figs, the number of sig figs you have for the given atomic masses.
