Question

How much energy is produced in the creation of 5 grams of "O by the process: (10 pts.) 14N + α. 'H + 170 ("N-14.00307 gmole, α-4.0026 gmol, 'H 1.00783 g/mole, 170-| 6.999 13 g/mol)

Answer 1

Answer : The energy produced is $3.410\times 10^{10}J$

Explanation :

First we have to calculate the moles of $^{17}O$.

$\text{Moles of }^{17}O=\frac{\text{Mass of }^{17}O}{\text{Molar mass of }^{17}O}=\frac{5g}{16.99913g/mole}=0.294133moles$

Now we have to calculate the mass defect.

The balanced reaction is,

$^{14}N+\alpha \rightarrow ^1H+^{17}O$

Mass defect = Sum of mass of product - sum of mass of reactants

$\Delta m=[(n_{^1H}\times M_{^1H})+(n_{^{17}O}\times M_{^{17}O})]-[(n_{^{14}N}\times M_{^{14}N})+(n_{\alpha}\times M_{\alpha})]$

where,

n = number of moles = 0.294133 moles

M = molar mass

Now put all the given values in the above, we get:

$\Delta m=[(n_{^1H}\times M_{^1H})+(n_{^{17}O}\times M_{^{17}O})]-[(n_{^{14}N}\times M_{^{14}N})+(n_{\alpha}\times M_{\alpha})]$

$\Delta m=[(0.294133mole\times 1.00783g/mole)+(0.294133mole\times 16.99913g/mole)]-[(0.294133mole\times 14.00307g/mole)+(0.294133mole\times 4.0026g/mole)]$

$\Delta m=0.00037943157g=3.7943157\times 10^{-7}kg$

Now we have to calculate the energy produced.

$Energy=\Delta m\times (c)^2$

$Energy=(3.7943157\times 10^{-7}kg)\times (299792458m/s)^2$

$Energy=3.410\times 10^{10}J$

Therefore, the energy produced is $3.410\times 10^{10}J$