2. A 500 mL saturated silver carbonate solution at 5¢XC is treated with hydrochloric acid to decompose the compound.
Ag2CO3(aq) + 2HCl(aq) ¡÷ 2AgCl(s) + CO2(g) + H2O(l)
The carbon dioxide generated is collected in a 19 mL vial and exerts a pressure of 114 mmHg at 25 ¢XC. What is the Ksp of Ag2CO3 at 5¢XC?
(Given: 1 atm = 760 mmHg)
Ag2CO3(aq) + 2HCl(aq) ¡÷ 2AgCl(s) + CO2(g) + H2O(l)
........Ag2CO3 ==> 2Ag^+ + CO3^2-
I.......solid........0......0
C.......solid.......2x......x
E.......solid.......2x......x
Use PV = nRT and solve for mols CO2 = mols CO3^2-. Then (CO3^2-) = mols/L of the saturated solution of Ag2CO3.
(Ag^+) = 2*(CO3^2-).
Substitute and solve for Ksp. Post your work if you get stuck.
0.97
My answer is 1.24792 x 10^-10
is it correct?
Updated, 4.9917x 10^-10?
To find the Ksp (solubility product constant) of Ag2CO3 at 5°C, we need to determine the concentration of Ag+ in the saturated solution after the decomposition reaction with hydrochloric acid.
First, let's determine the number of moles of CO2 generated. We can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
Pressure of CO2 (P) = 114 mmHg
Volume (V) = 19 mL = 0.019 L
Temperature (T) = 25°C = 298 K (since the temperature is given in Celsius, we need to convert it to Kelvin)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
Using the ideal gas law equation, we can rearrange it to solve for moles (n):
n = PV / RT
n = (114 mmHg * 0.019 L) / (0.0821 L·atm/(mol·K) * 298 K)
n = 0.0389 mol
Since the stoichiometry of the reaction is 1 mole of Ag2CO3 produces 1 mole of CO2, the number of moles of Ag2CO3 decomposed is also 0.0389 mol.
Next, we need to calculate the concentration of Ag+ ions in the solution. Since Ag2CO3 dissociates into 2Ag+ ions and 1 CO3^2- ion, each mole of Ag2CO3 produces 2 moles of Ag+ ions.
The initial volume of the solution is 500 mL, which is equal to 0.500 L. Therefore, the concentration of Ag+ ions is:
[Ag+] = (0.0389 mol / 0.500 L) * 2
[Ag+] = 0.1556 M
Finally, we can use the definition of the solubility product constant (Ksp) to find its value. The solubility product expression for Ag2CO3 is:
Ksp = [Ag+]^2 * [CO3^2-]
Given that the concentration of [Ag+] is 0.1556 M, we need to determine the concentration of [CO3^2-]. Since Ag2CO3 is a sparingly soluble salt, we can assume that the concentration of [CO3^2-] is negligibly small compared to [Ag+]. Therefore, we can ignore the contribution of [CO3^2-] to the solubility product.
Hence, the Ksp of Ag2CO3 at 5°C is equal to the square of the concentration of Ag+:
Ksp = (0.1556 M)^2
Ksp = 0.0242 M^2
Therefore, the Ksp of Ag2CO3 at 5°C is 0.0242 M^2.