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.
Well, it seems like Ci and Sd go together like cookies and cream! To find the strength of the Ci-Sd bond, we can use a little math and humor.
Since the solution is endothermic (meaning it absorbs heat), we know that the formation of the Ci-Sd bond must require an input of energy. We can calculate this energy by adding up the bond energies for the individual bonds broken and formed during the mixing process.
Since 40% of the solution is Ci and 60% is Sd, we'll need to break 40% of the Ci-Ci bonds and 60% of the Sd-Sd bonds. The energy required to break the Ci-Ci bonds would be: 0.4 * (-245 kJ/mol). And the energy required to break the Sd-Sd bonds would be: 0.6 * (-191 kJ/mol).
Now, since we are forming 1 mole of the Ci-Sd bond when the solution is mixed, we can set up an equation to find the energy released when the Ci-Sd bond is formed:
(0.4 * (-245 kJ/mol)) + (0.6 * (-191 kJ/mol)) + J-R = -44.6 kJ/mol
Simplifying the equation, we have:
(-98 kJ/mol) + (-114.6 kJ/mol) + J-R = -44.6 kJ/mol
Combining the like terms, we get:
-J-R = -44.6 kJ/mol + 98 kJ/mol + 114.6 kJ/mol
Solving the equation, we find:
J-R = 167 kJ/mol
So, the strength of the Ci-Sd bond is 167 kJ/mol.
And there you have it – the bond between Ci and Sd is a solid and attractive 167 kJ/mol! Keep mixing things up, my friend!
To find the strength of the Ci-Sd bond, we can use the concept of bond enthalpy. Bond enthalpy is the energy required to break one mole of a particular chemical bond in the gas phase.
Since the solution formation is an endothermic process, we can conclude that breaking the Ci-Sd bond requires energy. This energy is equal to the heat absorbed by the solution.
Given:
Bond energy of Ci-Ci bond = -245 kJ/mol
Bond energy of Sd-Sd bond = -191 kJ/mol
Heat absorbed by the solution = 44.6 kJ/mol
The energy required to break the Ci-Ci bonds in the cimium component is given by:
(40/100) * (-245) = -98 kJ/mol
Similarly, the energy required to break the Sd-Sd bonds in the sadowium component is given by:
(60/100) * (-191) = -114.6 kJ/mol
The remaining energy, 44.6 kJ/mol, is the energy required to break the Ci-Sd bond. Therefore, the strength of the Ci-Sd bond can be calculated as follows:
Ci-Sd bond energy = Heat absorbed by solution - energy required for Ci-Ci bonds - energy required for Sd-Sd bonds
= 44.6 kJ/mol - (-98 kJ/mol) - (-114.6 kJ/mol)
= 44.6 kJ/mol + 98 kJ/mol - 114.6 kJ/mol
= 27 kJ/mol
Hence, the strength of the Ci-Sd bond is 27 kJ/mol.
To find the strength of the Ci-Sd bond, we can start by calculating the energy change of the mixing process.
Given that a 40% cimium (Ci) and 60% sadowium (Sd) solution is an endothermic process that draws 44.6 kJ/mol of heat when mixed, we can assume that the energy change is due to breaking the Ci-Ci and Sd-Sd bonds and forming the Ci-Sd bonds.
Let's calculate the energy change for the mixing process:
Energy change = Energy to break Ci-Ci bonds + Energy to break Sd-Sd bonds - Energy to form Ci-Sd bonds
We are given the bond energies for Ci-Ci (-245 kJ/mol) and Sd-Sd (-191 kJ/mol). However, the bond energy for Ci-Sd is unknown.
Let's represent the unknown bond energy of Ci-Sd as J-R (in kJ/mol).
Energy change = (-245 kJ/mol) + (-191 kJ/mol) - J-R
Given that the energy change is +44.6 kJ/mol:
44.6 kJ/mol = (-245 kJ/mol) + (-191 kJ/mol) - J-R
Now, let's solve for J-R (the strength of the Ci-Sd bond):
J-R = (-245 kJ/mol) + (-191 kJ/mol) - 44.6 kJ/mol
J-R = -436 kJ/mol - 44.6 kJ/mol
J-R = -480.6 kJ/mol
Therefore, the strength of the Ci-Sd bond (J-R) is -480.6 kJ/mol.