1 mole of nitrogen and 3 moles of hydrogen were mixed at 593k and 2.0x10^7pa.At equilibrium the mixture contain 1.5 mole of ammonia.
1. Write the equilibrium expression for Kc
2. Find the mole fraction of each component and thus their molar concentration.
1. The equation for the reaction is:
N2(g) + 3H2(g) ⇌ 2NH3(g)
The equilibrium expression for Kc is:
Kc = [NH3]^2 / [N2] [H2]^3
2. To find the mole fraction of each component, we first need to calculate the total number of moles in the mixture:
Total moles = 1 mole of N2 + 3 moles of H2 = 4 moles
The mole fraction of N2 is:
X(N2) = moles of N2 / total moles = 1 / 4 = 0.25
The mole fraction of H2 is:
X(H2) = moles of H2 / total moles = 3 / 4 = 0.75
To calculate the molar concentration of each component, we need to use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.31 J/mol/K), and T is the temperature (593 K).
For N2:
n(N2) = PV / RT = (2.0x10^7 Pa)(1.0 L) / (8.31 J/mol/K)(593 K) = 0.521 mol
The molar concentration of N2 is:
[N2] = n(N2) / V = 0.521 mol / 1.0 L = 0.521 M
For H2:
n(H2) = PV / RT = (2.0x10^7 Pa)(1.0 L) / (8.31 J/mol/K)(593 K) = 1.563 mol
The molar concentration of H2 is:
[H2] = n(H2) / V = 1.563 mol / 1.0 L = 1.563 M
For NH3:
n(NH3) = 1.5 mol
The molar concentration of NH3 is:
[NH3] = n(NH3) / V = 1.5 mol / 1.0 L = 1.5 M
1. The equilibrium expression for Kc can be written as:
Kc = [NH3] / ([N2] * [H2]^3)
where [NH3], [N2], and [H2] represent the molar concentrations of ammonia, nitrogen, and hydrogen, respectively.
2. To find the mole fraction of each component and their molar concentrations, we need to use the ideal gas law and the concept of mole fraction.
First, let's calculate the total number of moles in the mixture:
Total moles = 1 mole (nitrogen) + 3 moles (hydrogen) + 1.5 moles (ammonia) = 5.5 moles
Next, we'll calculate the mole fraction of each component:
Mole fraction of ammonia (XNH3) = 1.5 / 5.5 = 0.2727
Mole fraction of nitrogen (XN2) = 1 / 5.5 ≈ 0.1818
Mole fraction of hydrogen (XH2) = 3 / 5.5 ≈ 0.5455
To convert the mole fractions into molar concentrations, we need to multiply each mole fraction by the total pressure (2.0x10^7 Pa) and divide by the ideal gas constant (R) times the temperature in Kelvin (593 K).
Molar concentration of ammonia ([NH3]) = XNH3 * (total pressure) / (R * temperature) = 0.2727 * (2.0x10^7 Pa) / (8.314 J/(mol⋅K) * 593 K) = 0.2741 mol/L
Molar concentration of nitrogen ([N2]) = XN2 * (total pressure) / (R * temperature) = 0.1818 * (2.0x10^7 Pa) / (8.314 J/(mol⋅K) * 593 K) = 0.1818 mol/L
Molar concentration of hydrogen ([H2]) = XH2 * (total pressure) / (R * temperature) = 0.5455 * (2.0x10^7 Pa) / (8.314 J/(mol⋅K) * 593 K) = 0.5469 mol/L
Therefore, the molar concentrations of ammonia, nitrogen, and hydrogen are approximately 0.2741 mol/L, 0.1818 mol/L, and 0.5469 mol/L, respectively.