Consider the equilibrium system described by the chemical reaction below. For this reaction, [tex]K_p = 4.51 \times 10^{x}[/tex] at a particular temperature. Calculate the value of [tex]Q_p[/tex] for the initial set of reaction conditions: 57 atm NH$_3$, 27 atm N$_2$, and 82 atm H$_2$.

Based on the given data, set up the expression for [tex]Q_p[/tex] and then evaluate it. Do not combine or simplify terms.

Reaction: [tex]N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)[/tex]

Expression for [tex]Q_p[/tex]:
\[ Q_p = \frac{(P_{NH_3})^2}{(P_{N_2})(P_{H_2})^3} \]

Substitute the values:
\[ Q_p = \frac{(57)^2}{(27)(82)^3} \]

Note: Ensure that you maintain correct units and check the exponent for [tex]K_p[/tex] as provided in the original question.

To calculate Qp for the given equilibrium system, the reaction quotient expression is set up with the provided pressures, and arithmetic operations are performed to find the numeric value of Qp = 1.457×10^−9 atm^−1.

Explanation:

The calculation of the reaction quotient, Qp, for the equilibrium system represented by the chemical reaction N2(g) + 3 H2(g) ↔ 2 NH3(g), requires the expression: Qp = (PNH3)2 / (PN2 * PH23).

Given the initial pressures, we substitute into this expression to find Qp: Qp = ((57 atm)2) / ((27 atm) * (82 atm)3) = 1.457×10^−9 atm^−1.

Following this, the calculation of Qp is simply a matter of applying basic arithmetic operations to these pressure values to get the numerical value of Qp. Without combining or simplifying terms, the numeric value of Qp must be calculated using the given pressures, leading to a direct comparison with Kp to predict the direction of the reaction.