A 10.0 L container contains 1.0 L of solution of a gas. Assume [gas]=1.5x10^-4 M in solution when 2 mol of gas remain in gas form. If 1 mol of gas is removed from the gas phase, what will be the new concentration of the gas in solution? What is the value of k?
To find the new concentration of the gas in solution, we need to use the equation for molarity:
Molarity = moles of solute / volume of solution in liters
1. First, we need to find the current concentration of the gas in solution. We are given that the volume of the container is 10.0 L and it contains 1.0 L of the gas solution. So, we can calculate the initial moles of gas in the solution:
moles of gas = concentration (Molarity) x volume of solution
moles of gas = (1.50 x 10^-4 M) x (1.0 L)
moles of gas = 1.50 x 10^-4 mol
2. We are also given that when 2 mol of gas remains in the gas form, the concentration of the gas in solution is 1.50 x 10^-4 M. From this, we can find the value of k, which represents the equilibrium constant:
k = concentration of gas in solution / moles of gas in the gas phase
k = (1.50 x 10^-4 M) / 2 mol
k = 7.50 x 10^-5 M/mol
3. Now, to find the new concentration of the gas in solution after removing 1 mol of gas from the gas phase, we can use the equation:
new concentration = (moles of gas - moles of gas removed) / volume of solution
new concentration = (1.50 x 10^-4 mol - 1 mol) / (1.0 L)
new concentration = -0.5 x 10^-4 M
Note that the negative sign indicates that there is no longer any gas in the solution.
Therefore, the new concentration of the gas in solution after removing 1 mol of gas from the gas phase is -0.5 x 10^-4 M, and the value of k is 7.50 x 10^-5 M/mol.
To find the new concentration of the gas in solution after removing 1 mol of gas from the gas phase, we can use the equation for concentration:
C = n/V
Where C is the concentration, n is the number of moles, and V is the volume.
Given:
Initial volume (V_initial) = 10.0 L
Initial gas remaining in the gas phase (n_initial gas) = 2 mol
Initial gas concentration (C_initial gas) = 1.5x10^-4 M
We can find the initial number of moles in the entire solution using the initial gas concentration and the initial volume:
n_initial solution = C_initial gas * V_initial
n_initial solution = (1.5x10^-4 M) * (10.0 L)
n_initial solution = 1.5x10^-3 mol
Now, to find the new concentration of the gas in solution after removing 1 mol from the gas phase, we need to subtract 1 mol from the initial number of moles in the solution:
n_new solution = n_initial solution - 1 mol
n_new solution = 1.5x10^-3 mol - 1 mol
n_new solution = 0.5x10^-3 mol
Finally, we can calculate the new concentration (C_new gas) by dividing the number of moles in the solution by the volume of the solution:
C_new gas = n_new solution / V_initial
C_new gas = (0.5x10^-3 mol) / (10.0 L)
C_new gas = 5x10^-5 M
The new concentration of the gas in solution after removing 1 mol of gas from the gas phase is 5x10^-5 M.
Now, let's calculate the value of k. The molar concentration (M) is defined as the moles of solute per liter of solution. Therefore, the concentration of the gas in solution can be expressed as the ratio of the number of moles of gas in solution (n_new solution) to the volume of the solution (V_initial).
C_new gas = n_new solution / V_initial
C_new gas = 5x10^-5 M
From the given information, we know that the concentration of the gas in solution when 2 mol of gas remain in the gas phase is 1.5x10^-4 M. Using this information, we can set up a ratio and solve for the value of k:
(1.5x10^-4 M) / (2 mol) = (5x10^-5 M) / (k mol)
(1.5x10^-4 M) / (2 mol) = (5x10^-5 M) / (k mol)
Cross-multiplying:
(1.5x10^-4 M) * (k mol) = (5x10^-5 M) * (2 mol)
1.5x10^-4 M * k mol = 1x10^-4 M * mol
Dividing both sides by 1.5x10^-4 M:
k mol = (1x10^-4 M * mol) / (1.5x10^-4 M)
k mol = 2/3 mol
Therefore, the value of k is 2/3 mol.
In summary:
The new concentration of the gas in solution after removing 1 mol of gas from the gas phase is 5x10^-5 M.
The value of k is 2/3 mol.