Two new metallic elements have been discovered, Cimium (Ci) and Sadowium (Sd). Both the pure elements and their solutions form simple cubic lattices. The bond strengths of the Ci-Ci and Sd-Sd bonds are known, but not the Ci-Sd bond.
Bond Bond Energy (kJ/mole)
Ci-Ci -245
Sd-Sd -191
J-R ??
Mixing a solution of 40% cimium and 60% sadowium is an endothermic process. According to your calorimeter, the solution draws 44.6 kJ/mol of heat when mixed. What is the strength of the Ci-Sd bond? Please give your answer in kJ/mol.
To determine the strength of the Ci-Sd bond, we can use the concept of bond energy and the given information.
1. First, let's understand the concept of bond energy. Bond energy refers to the amount of energy required to break a specific type of chemical bond in a mole of gaseous molecules. The negative value indicates that energy is released when the bond is formed, and the positive value indicates that energy is required to break the bond.
2. Given that the bond energy of Ci-Ci bond is -245 kJ/mol, and the bond energy of Sd-Sd bond is -191 kJ/mol, we need to find the strength of the Ci-Sd bond, denoted as J-R.
3. Since mixing a solution of 40% cimium (Ci) and 60% sadowium (Sd) is an endothermic process, it means that energy is absorbed. The heat absorbed during the process is 44.6 kJ/mol.
4. We can set up an equation to relate the bond energies and the heat absorbed during the reaction:
Total heat absorbed = (number of Ci-Ci bonds) * (bond energy of Ci-Ci) + (number of Sd-Sd bonds) * (bond energy of Sd-Sd) + (number of Ci-Sd bonds) * (bond energy of Ci-Sd)
Substituting the given values, the equation becomes:
44.6 kJ/mol = (0.4 * n) * (-245 kJ/mol) + (0.6 * n) * (-191 kJ/mol) + n * (J-R)
Here, 'n' represents the number of moles (which cancels out in the calculation).
5. Simplifying the equation, we get:
44.6 kJ/mol = -98n - 114.6n + n * (J-R)
6. Rearranging the terms, we have:
J-R * n = 44.6 kJ/mol + 98n + 114.6n
7. Factoring out 'n' from the right side of the equation:
J-R * n = 44.6 kJ/mol + 212.6n
8. Dividing both sides by 'n', we get:
J-R = (44.6 kJ/mol + 212.6n) / n
The value of 'n' cancels out, leaving us with:
J-R = 44.6 kJ/mol / n + 212.6
9. Since we know that 'n' is equal to 1, as we are considering the formation of one mole of the Ci-Sd bond, the equation becomes:
J-R = 44.6 kJ/mol / 1 + 212.6
J-R = 44.6 kJ/mol + 212.6
10. Calculating the value, we find:
J-R = 257.2 kJ/mol
Therefore, the strength of the Ci-Sd bond is 257.2 kJ/mol.