The values of `Delta H` and `Delta S` for the reaction
are `170 kJ` and `170 J K^(-1)`, respectively. This reaction will be spontaneous at

Options

A. `910 K`
B. `1110 K`
C. `510 K`
D. `710 K`

Explanation

To determine the temperature at which the reaction will be spontaneous, we can use the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- \(\Delta G\) is the change in Gibbs free energy,
- \(\Delta H\) is the change in enthalpy,
- \(T\) is the temperature in Kelvin,
- \(\Delta S\) is the change in entropy.

For a reaction to be spontaneous, \(\Delta G\) must be less than zero:

\[ \Delta G < 0 \]

Substituting the expression for \(\Delta G\):

\[ \Delta H - T \Delta S < 0 \]

Rearranging this inequality gives:

\[ \Delta H < T \Delta S \]

Now, substituting the given values:

- \(\Delta H = 170 \, \text{kJ} = 170 \times 10^3 \, \text{J}\) (since 1 kJ = 1000 J)
- \(\Delta S = 170 \, \text{J K}^{-1}\)

We can rewrite the inequality as:

\[ 170 \times 10^3 < T \times 170 \]

Dividing both sides by 170:

\[ 1000 < T \]

This implies:

\[ T > 1000 \, \text{K} \]

Thus, the reaction will be spontaneous at temperatures greater than 1000 K.

### Summary of Steps:
1. Write the Gibbs free energy equation.
2. Set the condition for spontaneity (\(\Delta G < 0\)).
3. Rearrange the equation to find the relationship between \(\Delta H\), \(\Delta S\), and \(T\).
4. Substitute the given values of \(\Delta H\) and \(\Delta S\).
5. Solve the inequality to find the temperature condition for spontaneity.