At `445^(@)C,K_(c)` for the following reaction is `0.020`.
`2HI(g)rarrH_(2)(g)+I_(2)(g)`
A mixture of `H_(2),I_(2)` and `HI` in a vessel at `445^(@)C` has the following concentration: `[HI]=2.0M,[H_(2)]=0.50M` and `[I_(2)]=0.10M`. The statement that is true concerning the reaction quotient, `Q_(c)` is:

Options

A. `Q_(c)K_(c),` the system is at equilibrium
B. `Q_(c)` less than `K_(c),` more `H_(2) "and" I_(2)` will be produced
C. `Q_(c)` less than `K_(c),` more `HI` will be produced
D. `Q_(c)` is greater than `K_(c),` more `H_(2) "and" I_(2)` will be produced

Answer

To solve the problem step by step, we will first write down the reaction and the given information, then we will calculate the reaction quotient \( Q_c \), and finally, we will compare \( Q_c \) with \( K_c \) to determine the direction of the reaction.

### Step 1: Write down the reaction and the given information
The reaction is:
\[ 2 \text{HI}(g) \rightleftharpoons \text{H}_2(g) + \text{I}_2(g) \]

Given concentrations at \( 445^\circ C \):
- \([HI] = 2.0 \, M\)
- \([H_2] = 0.50 \, M\)
- \([I_2] = 0.10 \, M\)

The equilibrium constant \( K_c \) for the reaction is given as:
\[ K_c = 0.020 \]

### Step 2: Calculate the reaction quotient \( Q_c \)
The reaction quotient \( Q_c \) is calculated using the formula:
\[ Q_c = \frac{[\text{products}]}{[\text{reactants}]^n} \]
For the given reaction:
\[ Q_c = \frac{[\text{H}_2][\text{I}_2]}{[\text{HI}]^2} \]

Substituting the values:
\[ Q_c = \frac{(0.50)(0.10)}{(2.0)^2} \]
Calculating the numerator:
\[ 0.50 \times 0.10 = 0.05 \]
Calculating the denominator:
\[ (2.0)^2 = 4.0 \]
Now substituting these values into the equation for \( Q_c \):
\[ Q_c = \frac{0.05}{4.0} = 0.0125 \]

### Step 3: Compare \( Q_c \) with \( K_c \)
We have:
- \( Q_c = 0.0125 \)
- \( K_c = 0.020 \)

Since \( Q_c < K_c \), this indicates that the reaction will proceed in the forward direction to reach equilibrium. This means that more products (\( H_2 \) and \( I_2 \)) will be produced.

### Conclusion
The statement that is true concerning the reaction quotient \( Q_c \) is:
- \( Q_c < K_c \) implies that more \( H_2 \) and \( I_2 \) will be produced.