5)

Hydrogen can be produced by the steam reforming of methane as follows:
$$
\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CH}_{4}(\mathrm{~g})=\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})
$$
a) If $K_{c}$ is $3.8 \times 10^{-3}$ at $1000 \mathrm{~K}$, what is the value of $K_{p}$ ?
b) If $K_{p}$ is $6.1 \times 10^{4}$ at $1125^{\circ} \mathrm{C}$, what is the value of $K_{c}$ ?
$[26,4.6]$

Question

5)

Hydrogen can be produced by the steam reforming of methane as follows:
$$
\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CH}_{4}(\mathrm{~g})=\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})
$$
a) If $K_{c}$ is $3.8 \times 10^{-3}$ at $1000 \mathrm{~K}$, what is the value of $K_{p}$ ?
b) If $K_{p}$ is $6.1 \times 10^{4}$ at $1125^{\circ} \mathrm{C}$, what is the value of $K_{c}$ ?
$[26,4.6]$

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Identify the relationship between $K_p$ and $K_c$**: The relationship between the equilibrium constants $K_p$ and $K_c$ is given by the equation $K_p = K_c(RT)^{\Delta n}$, where $R$ is the ideal gas constant (0.0821 L·atm/mol·K), $T$ is the temperature in Kelvin, and $\Delta n$ is the change in the number of moles of gas in the reaction. ‖ ‖ 2 ⋮ **Calculate $\Delta n$ for the reaction**: For the given reaction, $\Delta n = (1 + 3) - (1 + 1) = 2$. ‖ ‖ 3 ⋮ **Calculate $K_p$ using $K_c$**: Given $K_c = 3.8 imes 10^{-3}$ at $T = 1000$ K, we use the equation from step 1 to find $K_p = K_c(RT)^{\Delta n} = 3.8 imes 10^{-3} imes (0.0821 imes 1000)^2$. ‖ ∻a Answer∻ ⚹ $K_p = 3.1 imes 10^{2}$ ⚹ ∻Key Concept∻ ⚹ The relationship between $K_p$ and $K_c$ involves the temperature and the change in the number of moles of gas. ⚹ ∻Explanation∻ ⚹ $K_p$ is calculated from $K_c$ by considering the change in moles of gas and the temperature in Kelvin. ⚹ ‖ 1 ⋮ **Identify the relationship between $K_p$ and $K_c$ for part b**: The relationship is the same as in part a, $K_p = K_c(RT)^{\Delta n}$. ‖ ‖ 2 ⋮ **Convert temperature to Kelvin**: The temperature is given as 1125°C, which is 1125 + 273.15 = 1398.15 K. ‖ ‖ 3 ⋮ **Calculate $K_c$ using $K_p$**: Given $K_p = 6.1 imes 10^{4}$, we rearrange the equation from step 1 to find $K_c = \frac{K_p}{(RT)^{\Delta n}} = \frac{6.1 imes 10^{4}}{(0.0821 imes 1398.15)^2}$. ‖ ∻b Answer∻ ⚹ $K_c = 3.3 imes 10^{-2}$ ⚹ ∻Key Concept∻ ⚹ The relationship between $K_p$ and $K_c$ is used to calculate one from the other, given the temperature and the change in moles of gas. ⚹ ∻Explanation∻ ⚹ $K_c$ is calculated from $K_p$ by using the ideal gas constant and the temperature in Kelvin, along with the change in moles of gas. ⚹◊What is the relationship between $K_p$ and $K_c$ in the context of chemical equilibrium⍭ Generate me a similar question◊

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