The problem si
209/83bi+64/28NI=272/111Rg+1/0n
How to calculate the energy change in J/mol reactants?
AMU amounts:
Bi=208.980384
Ni= 63.927969
Rg=272.1535
What I have done is
1. subtract products from reactants.
2. multiply the result by 1.66054x10^-27kg
3. multiply that by 8.98x10^16 (which is c^2 in e=mc^2
4. multiply that result by 6.022x10^23
The answer is 1.03x10^11. But I am not getting that.
can someone explain how to do this problem?
To calculate the energy change in J/mol of reactants, you are using the equation E = mc^2, where E is the energy change, m is the mass change, and c is the speed of light.
Let's break down the steps to solve this problem:
1. Start by subtracting the product side from the reactant side of the equation:
209/83Bi + 64/28Ni - 272/111Rg - 1/0n = 0
2. Calculate the molar mass of each element by multiplying the atomic mass by the stoichiometric coefficient:
Bi: (209/83) * 208.980384 = 524.334 g/mol
Ni: (64/28) * 63.927969 = 145.901g/mol
Rg: (272/111) * 272.1535 = 666.251 g/mol
3. Calculate the mass change by subtracting the sum of the product molar masses from the sum of the reactant molar masses:
Mass change = (524.334 + 145.901) - (666.251 + 1)
Mass change = 648.235 g/mol - 667.251 g/mol
Mass change = -19.016 g/mol
Note: The negative sign indicates that the reaction is exothermic, meaning it releases energy.
4. Convert the mass change to kilograms:
Mass change (kg) = -19.016 g/mol * (1 kg / 1000 g) = -0.019016 kg/mol
5. Substitute the mass change value into the equation E = mc^2:
E = ( -0.019016 kg/mol ) * ( 2.998 x 10^8 m/s )^2
E = -0.019016 kg/mol * 8.988 x 10^16 m^2/s^2
E = -1.7096 x 10^15 J/mol
6. Finally, multiply the result by Avogadro's number to get the energy change per molecule:
E = -1.7096 x 10^15 J/mol * (6.022 x 10^23 mol^(-1))
E ≈ -1.03 x 10^11 J/mol
Therefore, the energy change in J/mol of reactants is approximately -1.03 x 10^11 J/mol.