Answer:
Total pressure for both systems is 14.26atm.
Explanation:
Kp for the reaction is:
[tex]K_P = 0.263 = \frac{P_{CH_4}}{P_H_{2}^2}[/tex]
As C is a pure solid, is not taken into account for Kp expression.
5.207g of H₂ are:
5.207g ₓ (1 mol / 2.01g) = 2.59moles of gas.
Using PV = nRT:
P = 2.59molₓ0.082atmL/molKₓ1000K / 9.32L = 22.8atm
The expressions for pressure in equilibrium are:
P{H₂} = 22.8atm - 2X
P{CH₄} = X
Replacing in Kp expression:
0.263 = X / (22.8 - 2X)²
0.263 = X / 520 - 91.2X +4X²
136.8 - 24X + 1.052X² = X
Solving for X:
X = 8.54atm → Right solution
X = 15.22atm → False solution. Because produce a negative concentration.
Replacing:
P{H₂} = 22.8atm - 2*8.54atm = 5.72atm
P{CH₄} = 8.54atm
Pressure of H₂ is 5.72atm and pressure of CH₄ is 8.54atm. Total pressure is:
5.72atm + 8.54atm = 14.26atm
As mass of Carbon is not taken into account is Kp expression and mass of hydrogen is the same with the same volume, total pressure is also 14.26atm
The total pressure is the sum of the static and the velocity pressure exerted in a system. The total pressure of both systems is 14.26 atm.
The pressure exerted by the substance on the surface of the system is called the total pressure. It is equivalent to the total of the free dynamic and the static pressure.
Kp for the reaction between carbon and hydrogen can be shown as:
[tex]\rm K_{p} = \dfrac{P_{CH_{4}}}{P_{H_{2}^{2}}}[/tex]
Given,
Calculate the moles of hydrogen gas:
[tex]\begin{aligned}\rm Moles &= 5.207 \times \dfrac{1\;\rm mol}{2.01\;\rm g}\\\\&= 2.59\;\rm mol\end{aligned}[/tex]
The formula for the ideal gas equation is:
PV = nRT
Substituting values in the above formula:
[tex]\begin{aligned}\rm P &= \dfrac{2.59\;\rm mol \times 0.082\;\rm atmL/molK \times 1000 K}{9.32\;\rm L}\\\\&=22.8\;\rm atm \end{aligned}[/tex]
Substituting values in the Kp equation:
[tex]\begin{aligned}0.263 &= \dfrac{\rm X }{(22.8 - 2\rm X)^{2}}\\\\0.263 &= \dfrac{\rm X }{ 520 - 91.2\rm X +4\rm X^{2}}\\\\136.8 - 25\rm X + 1.052\rm X^{2}&= 0\end{aligned}[/tex]
The pressure in equilibrium can be shown as:
[tex]\begin{aligned}\rm P_{H_{2}} &= 22.8\;\rm atm - 2X\\\\\rm P_{CH_{4}} &= \rm X\end{aligned}[/tex]
Substituting the value of X in the above equation:
[tex]\begin{aligned}\rm P_{H_{2}} &= 22.8\rm atm - (2\times 8.54)\\\\\rm P_{H_{2}} &=5.72\;\rm atm\\\\\rm P_{CH_{4}} &= 8.54 \end{aligned}[/tex]
The pressure of the hydrogen is 5.72 atm and that of methane is 8.54 atm.
The total pressure of the system is:
5.72atm + 8.54atm = 14.26atm
Therefore, 14.26 atm is the total pressure of the system.
Learn more about Kp and total pressure here:
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