For homogeneous gas reaction `4NH_(3) + 5O_(2)hArr4NO + 6H_(2)O`. The equilibrium constant `K_(c)` has the unit of

Options

A. `("concentration")^(1)`
B. `("concentration")^(-1)`
C. `("concentration")^(9)`
D. `("concentration")^(10)`

Explanation

To determine the units of the equilibrium constant \( K_c \) for the given reaction \( 4NH_3 + 5O_2 \rightleftharpoons 4NO + 6H_2O \), we will follow these steps:

### Step 1: Write the expression for the equilibrium constant \( K_c \)

The equilibrium constant \( K_c \) is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced equation.

For the reaction:
\[ 4NH_3 + 5O_2 \rightleftharpoons 4NO + 6H_2O \]

The expression for \( K_c \) is:
\[ K_c = \frac{[NO]^4 [H_2O]^6}{[NH_3]^4 [O_2]^5} \]

### Step 2: Determine the units of concentration

The concentration of a substance is typically measured in moles per liter (mol/L), which can also be expressed as \( M \) (molarity).

### Step 3: Substitute the units into the \( K_c \) expression

Now, we will substitute the units into the \( K_c \) expression:

- The numerator consists of \( [NO]^4 \) and \( [H_2O]^6 \):
- Units for \( [NO] \): \( M \)
- Units for \( [H_2O] \): \( M \)

Thus, the units for the numerator will be:
\[ (M^4)(M^6) = M^{4+6} = M^{10} \]

- The denominator consists of \( [NH_3]^4 \) and \( [O_2]^5 \):
- Units for \( [NH_3] \): \( M \)
- Units for \( [O_2] \): \( M \)

Thus, the units for the denominator will be:
\[ (M^4)(M^5) = M^{4+5} = M^{9} \]

### Step 4: Combine the units to find the units of \( K_c \)

Now we can combine the units from the numerator and denominator:
\[ K_c = \frac{M^{10}}{M^{9}} = M^{10-9} = M^{1} \]

### Conclusion

The units of the equilibrium constant \( K_c \) for the given reaction are \( M \) (molarity).

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