Values of heats of formation for `SiO_(2)` and `MgO` are `-48.4` and `-34.7 kJ` respectively. The heat of the reaction `2Mg+SiO_(2)rarr2MgO+Si` is

Options

A. 21.16 kJ
B. `-21.10 kJ`
C. `-13.62 kJ`
D. 13.6 kJ

Answer

To find the heat of the reaction for the given equation \(2Mg + SiO_2 \rightarrow 2MgO + Si\), we will use the heats of formation provided for \(SiO_2\) and \(MgO\). The heat of reaction can be calculated using the formula:

\[ \Delta H_{reaction} = \Delta H_f (products) - \Delta H_f (reactants) \]

### Step-by-Step Solution:

1. **Identify the products and their heats of formation:**
- The products of the reaction are \(2MgO\) and \(Si\).
- The heat of formation for \(MgO\) is given as \(-34.7 \, kJ/mol\).
- The heat of formation for \(Si\) is considered to be \(0 \, kJ/mol\) (as it is in its standard state).

2. **Calculate the total heat of formation for the products:**
- For \(2MgO\):
\[ \Delta H_f (2MgO) = 2 \times (-34.7 \, kJ/mol) = -69.4 \, kJ \]
- For \(Si\):
\[ \Delta H_f (Si) = 0 \, kJ/mol \]
- Therefore, the total heat of formation for the products is:
\[ \Delta H_f (products) = -69.4 \, kJ + 0 \, kJ = -69.4 \, kJ \]

3. **Identify the reactants and their heats of formation:**
- The reactants are \(2Mg\) and \(SiO_2\).
- The heat of formation for \(SiO_2\) is given as \(-48.4 \, kJ/mol\).
- The heat of formation for \(Mg\) is considered to be \(0 \, kJ/mol\).

4. **Calculate the total heat of formation for the reactants:**
- For \(2Mg\):
\[ \Delta H_f (2Mg) = 2 \times 0 \, kJ/mol = 0 \, kJ \]
- For \(SiO_2\):
\[ \Delta H_f (SiO_2) = -48.4 \, kJ/mol \]
- Therefore, the total heat of formation for the reactants is:
\[ \Delta H_f (reactants) = 0 \, kJ + (-48.4 \, kJ) = -48.4 \, kJ \]

5. **Substitute the values into the heat of reaction formula:**
\[ \Delta H_{reaction} = \Delta H_f (products) - \Delta H_f (reactants) \]
\[ \Delta H_{reaction} = (-69.4 \, kJ) - (-48.4 \, kJ) \]
\[ \Delta H_{reaction} = -69.4 \, kJ + 48.4 \, kJ = -21.0 \, kJ \]

### Final Answer:
The heat of the reaction \(2Mg + SiO_2 \rightarrow 2MgO + Si\) is \(-21.0 \, kJ\).