If the heat of combustion of carbon monoxide at constant volume and at `17^@`C is `-283.3`kJ, then its heat of combustion at constant pressure is _________ .
(R = 8.314 J `kelvin ^-1 mol^-1`)

Options

A. `-284.5 kJ`
B. `284.5 kJ`
C. `384.5 kJ`
D. `-384.5 kJ`

Answer

To find the heat of combustion of carbon monoxide at constant pressure, we can use the relationship between the change in internal energy (ΔE) and the change in enthalpy (ΔH). The formula we will use is:

\[ \Delta E = \Delta H - \Delta n_g RT \]

Where:
- ΔE is the change in internal energy (given as -283.3 kJ)
- ΔH is the change in enthalpy (what we need to find)
- Δn_g is the change in the number of moles of gas
- R is the gas constant (8.314 J K⁻¹ mol⁻¹)
- T is the temperature in Kelvin

### Step 1: Determine Δn_g
The combustion reaction of carbon monoxide can be represented as:

\[ \text{CO (g)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \]

In this reaction:
- The number of moles of gaseous products = 1 (from CO₂)
- The number of moles of gaseous reactants = 1 (from CO) + 0.5 (from O₂) = 1.5

Thus,

\[ \Delta n_g = \text{moles of products} - \text{moles of reactants} = 1 - 1.5 = -0.5 \]

### Step 2: Convert the temperature to Kelvin
The temperature given is 17°C. To convert this to Kelvin:

\[ T = 17 + 273 = 290 \text{ K} \]

### Step 3: Convert R to kJ
Since we need the final answer in kJ, we convert R from J to kJ:

\[ R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1} = 8.314 \times 10^{-3} \text{ kJ K}^{-1} \text{ mol}^{-1} \]

### Step 4: Substitute the values into the equation
Now we can substitute the values into the equation:

\[ \Delta H = \Delta E + \Delta n_g RT \]

Substituting the known values:

\[ \Delta H = -283.3 \text{ kJ} + (-0.5) \times (8.314 \times 10^{-3} \text{ kJ K}^{-1} \text{ mol}^{-1}) \times (290 \text{ K}) \]

Calculating the second term:

\[ \Delta H = -283.3 \text{ kJ} + (-0.5) \times (8.314 \times 10^{-3}) \times 290 \]

Calculating:

\[ = -283.3 \text{ kJ} + (-0.5) \times 2.41 \text{ kJ} \]
\[ = -283.3 \text{ kJ} - 1.205 \text{ kJ} \]
\[ = -284.505 \text{ kJ} \]

### Step 5: Round to appropriate significant figures
Rounding to three significant figures, we have:

\[ \Delta H \approx -284.5 \text{ kJ} \]

Thus, the heat of combustion of carbon monoxide at constant pressure is approximately **-284.5 kJ**.

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