Answer :
To solve this problem, we need to calculate the reaction quotient, [tex]\( Q_p \)[/tex], for the given reaction with the initial pressures provided:
The reaction is:
[tex]\[ \text{N}_2(g) + 3 \text{H}_2(g) \rightleftharpoons 2 \text{NH}_3(g) \][/tex]
The expression for the reaction quotient [tex]\( Q_p \)[/tex] is given by the formula:
[tex]\[ Q_p = \frac{(\text{Pressure of } \text{NH}_3)^2}{(\text{Pressure of } \text{N}_2) \times (\text{Pressure of } \text{H}_2)^3} \][/tex]
Let's plug in the initial pressures provided:
- Pressure of [tex]\(\text{NH}_3\)[/tex] = 57 atm
- Pressure of [tex]\(\text{N}_2\)[/tex] = 27 atm
- Pressure of [tex]\(\text{H}_2\)[/tex] = 82 atm
Now, we substitute these values into the expression for [tex]\( Q_p \)[/tex]:
[tex]\[ Q_p = \frac{(57)^2}{(27) \times (82)^3} \][/tex]
Next, calculate the powers and products:
- [tex]\( (57)^2 = 3249 \)[/tex]
- [tex]\( (82)^3 = 82 \times 82 \times 82 = 551368 \)[/tex]
Now, compute the denominator:
[tex]\[ 27 \times 551368 = 14886836 \][/tex]
Finally, calculate [tex]\( Q_p \)[/tex]:
[tex]\[ Q_p = \frac{3249}{14886836} \][/tex]
After performing the division, we get the value:
[tex]\[ Q_p = 0.00021824504384246698 \][/tex]
Based on these calculations, the value of [tex]\( Q_p \)[/tex] under the initial conditions is approximately [tex]\( 0.000218 \)[/tex].
The reaction is:
[tex]\[ \text{N}_2(g) + 3 \text{H}_2(g) \rightleftharpoons 2 \text{NH}_3(g) \][/tex]
The expression for the reaction quotient [tex]\( Q_p \)[/tex] is given by the formula:
[tex]\[ Q_p = \frac{(\text{Pressure of } \text{NH}_3)^2}{(\text{Pressure of } \text{N}_2) \times (\text{Pressure of } \text{H}_2)^3} \][/tex]
Let's plug in the initial pressures provided:
- Pressure of [tex]\(\text{NH}_3\)[/tex] = 57 atm
- Pressure of [tex]\(\text{N}_2\)[/tex] = 27 atm
- Pressure of [tex]\(\text{H}_2\)[/tex] = 82 atm
Now, we substitute these values into the expression for [tex]\( Q_p \)[/tex]:
[tex]\[ Q_p = \frac{(57)^2}{(27) \times (82)^3} \][/tex]
Next, calculate the powers and products:
- [tex]\( (57)^2 = 3249 \)[/tex]
- [tex]\( (82)^3 = 82 \times 82 \times 82 = 551368 \)[/tex]
Now, compute the denominator:
[tex]\[ 27 \times 551368 = 14886836 \][/tex]
Finally, calculate [tex]\( Q_p \)[/tex]:
[tex]\[ Q_p = \frac{3249}{14886836} \][/tex]
After performing the division, we get the value:
[tex]\[ Q_p = 0.00021824504384246698 \][/tex]
Based on these calculations, the value of [tex]\( Q_p \)[/tex] under the initial conditions is approximately [tex]\( 0.000218 \)[/tex].
