Given the standard heats of reaction

Reaction ∆H0
M(s) + 2 X2(g) → MX4(g) −123.7 kJ/mol
X2(g) → 2 X(g) +297.3 kJ/mol
M(g) → M(s) −25.1 kJ/mol
calculate the average bond energy for a single
M- X bond

To calculate the average bond energy for a single M-X bond, we can use the concept of Hess's law and the given standard heats of reaction.

Hess's law states that the change in enthalpy for a reaction is independent of the pathway taken.

Let's assume the M-X bond formation takes place in the following steps:

1. M(g) → M(s) (reverse of reaction 3)
Enthalpy change: +25.1 kJ/mol

2. X2(g) → 2 X(g) (reverse of reaction 2)
Enthalpy change: -297.3 kJ/mol

3. M(s) + 2 X(g) → MX4(g) (reverse of reaction 1)
Enthalpy change: +123.7 kJ/mol

Now, let's apply Hess's law to calculate the average bond energy of a single M-X bond.

Since we want to find the average bond energy for a single M-X bond, let's consider the reaction: MX4(g) → M(g) + 2 X2(g)

The enthalpy change for this reaction would be the reverse of reaction 1, therefore: ∆H = -123.7 kJ/mol

According to Hess's law, the enthalpy change of a reaction is equal to the sum of the enthalpy changes of its individual steps.

∆H = ∆H1 + ∆H2 + ∆H3

-123.7 kJ/mol = (+25.1 kJ/mol) + (-297.3 kJ/mol) + ∆H3

Simplifying, we get:

∆H3 = -123.7 kJ/mol -25.1 kJ/mol + 297.3 kJ/mol
= +148.5 kJ/mol

Now, we need to determine the number of M-X bonds formed in reaction 3. From the balanced equation, we can see that 2 X(g) react to form 1 MX4(g) molecule. Therefore, the number of M-X bonds formed is 4.

To calculate the average bond energy for a single M-X bond, we divide ∆H3 by the number of bonds:

Average bond energy for a single M-X bond = ∆H3/number of bonds
= 148.5 kJ/mol / 4
= 37.1 kJ/mol

Therefore, the average bond energy for a single M-X bond is 37.1 kJ/mol.

To calculate the average bond energy for a single M-X bond, we need to use the given standard heats of reaction. Bond energy refers to the energy required to break a bond, so we will need to consider the energy changes of the corresponding reactions involving the breaking and forming of M-X bonds.

The given reactions involve the formation or breaking of M-X bonds indirectly. We will need to manipulate the given reactions to determine the energy change for the breaking or formation of a single M-X bond.

1. The first reaction shows the formation of MX4(g) from M(s) and 2X2(g). The given standard heat of reaction (∆H0) is -123.7 kJ/mol. This reaction involves the formation of four M-X bonds because there is one M atom and four X atoms in the product.

2. The second reaction shows the formation of two X(g) molecules from one X2(g) molecule. The given ∆H0 is +297.3 kJ/mol. This reaction involves the breaking of one X-X bond to form two X atoms.

3. The third reaction shows the formation of M(s) from M(g). The given ∆H0 is -25.1 kJ/mol. This reaction involves the formation of one M-X bond, as M(g) is converted to M(s).

Now, let's manipulate these reactions to find the energy change for the breaking or formation of a single M-X bond:

a) Multiply the first reaction by 2 to balance the number of X atoms:
2M(s) + 4X2(g) → 2MX4(g) ΔH = -2*(123.7 kJ/mol) = -247.4 kJ/mol

b) Multiply the second reaction by 2 to balance the number of X atoms:
2X2(g) → 4X(g) ΔH = 2*(297.3 kJ/mol) = 594.6 kJ/mol

c) Since the goal is to determine the energy change for a single M-X bond, we can subtract the energy changes obtained in steps a) and b) to eliminate the multiple bonds and keep a single M-X bond:
2M(s) + 4X2(g) + 594.6 kJ/mol → 2MX4(g) + 247.4 kJ/mol

d) Finally, we can use the energy change from the third reaction to calculate the energy change for a single M-X bond:
2M(s) + 4X2(g) + 594.6 kJ/mol + (-25.1 kJ/mol) → 2MX4(g) + 247.4 kJ/mol + (-25.1 kJ/mol)

Here, the 2M(s) and 2MX4(g) cancel out, leaving the equation as:
4X2(g) + 594.6 kJ/mol + (-25.1 kJ/mol) → 247.4 kJ/mol + (-25.1 kJ/mol)

Simplifying further:
4X2(g) + 569.5 kJ/mol → 222.3 kJ/mol

Now, divide both sides by 4 to isolate the energy change for a single M-X bond:
X2(g) + 142.4 kJ/mol → 55.6 kJ/mol

Therefore, the average bond energy for a single M-X bond is approximately 55.6 kJ/mol.