If the initial pressure of HD(g) is 2.270 atm, calculate the % decomposition of HD(g) when the reaction comes to equilibrium according to the balanced equation. The value of Kp at 727.0 °C is 0.26. The initial pressure of the reaction products is 0 atm.
2HD(g) = H2(g)+D2(g)
............2HD ==> H2 + D2
initial.....2.270...0.....0
change......-2p.....p.....p
equil.....2.27-2p...p.....p
Substitute into Kp equation and solve for p. Then %decomp = (p/2.27)*100 = ?
To calculate the % decomposition of HD gas when the reaction comes to equilibrium, we need to use the concept of equilibrium and the value of Kp.
The balanced equation for the reaction is:
2HD(g) = H2(g) + D2(g)
The equation tells us that 2 moles of HD gas decompose to form 1 mole of H2 gas and 1 mole of D2 gas.
Now, let's calculate the moles of HD gas present initially. We know the initial pressure of HD gas is 2.270 atm. We can use the ideal gas law to calculate the moles:
PV = nRT
Where:
P = pressure (atm)
V = volume (L)
n = moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (Kelvin)
Since we don't have the volume and temperature information, we can't calculate the exact number of moles. However, we can calculate the ratio of moles of HD gas decomposed to the initial moles of HD gas.
Let's assume the initial moles of HD gas are "x" moles. Therefore, the initial moles of H2 and D2 gases are also "x/2" moles each.
At equilibrium, let's assume "y" moles of HD gas decompose. Therefore, the moles of H2 and D2 gases formed will be "y/2" moles each.
According to the balanced equation, the initial moles of HD gas minus the moles decomposed is equal to the moles of HD gas at equilibrium:
x - y = equilibrium moles of HD gas
The equilibrium pressure of HD gas can be calculated using the ideal gas law:
P(HD) = n(HD) * RT / V
Since the initial pressure of HD gas is 2.270 atm, we can write:
2.270 atm = (x - y) * (0.0821 L·atm/(mol·K)) * T / V
Now, we know the value of Kp for the reaction at 727.0 °C is 0.26. For a gaseous reaction, Kp is defined as the ratio of the partial pressures of the products to the partial pressures of the reactants, each raised to their stoichiometric coefficients.
In this case, the stoichiometric coefficient for HD gas is 2, and for H2 and D2 gases, it is 1 each.
So, Kp = (P(H2) * P(D2)) / (P(HD)^2)
Since the initial pressure of the reaction products (H2 and D2) is 0 atm, we can write:
Kp = (0 atm * 0 atm) / (2.270 atm)^2
Now, we can solve this equation to find the value of y, which represents the moles of HD gas decomposed at equilibrium. Once we have the value of y, we can calculate the % decomposition of HD gas using the formula:
% decomposition = (moles decomposed / initial moles) * 100
By substituting the values into these equations, you can find the % decomposition of HD gas when the reaction reaches equilibrium.