At 25 °C, only 1.9 g CaSO4 (MM = 136 g/mol) will dissolve in 2.00 L of water. Write the equilibrium
expression and calculate the equilibrium constant for the reaction below.
CaSO4 (s) ⇋ Ca2+ (aq) + SO42- (aq)
Ksp = (Ca^+2)(SO4^-2)
Solubility CaSO4 = S = 1.9g/136 = ??mole and that in 2L is ??/2 = (S)
Then substitute the value for S into the Ka expression and solve for Ka.
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The equilibrium expression for the reaction is:
K = [Ca2+][SO42-]
where [Ca2+] and [SO42-] represent the concentrations of Ca2+ and SO42- ions in the solution, respectively.
To calculate the equilibrium constant (K), we need to determine the concentrations of the ions. Since we are given the mass of CaSO4 (1.9 g) and the volume of the solution (2.00 L), we can use these values to find the concentration of Ca2+ and SO42- ions.
First, we need to convert the mass of CaSO4 to moles using its molar mass:
moles of CaSO4 = mass / molar mass = 1.9 g / 136 g/mol = 0.01397 mol
Since 1 mole of CaSO4 dissociates to give 1 mole of Ca2+ and 1 mole of SO42-, the concentrations of Ca2+ and SO42- ions are both equal to 0.01397 mol/L.
Substituting these values into the equilibrium expression, we have:
K = (0.01397 mol/L) * (0.01397 mol/L) = 0.0001947 mol^2/L^2
Therefore, the equilibrium constant (K) for the reaction is approximately 0.0001947 mol^2/L^2.
To write the equilibrium expression for the given reaction and calculate the equilibrium constant (K), you need to understand the concept of solubility product constant (Ksp) and how it relates to the equilibrium expression.
First, let's write the balanced equation for the reaction:
CaSO4 (s) ⇋ Ca2+ (aq) + SO42- (aq)
The equilibrium expression can be written using the concentrations of the ions involved:
K = [Ca2+] * [SO42-]
In this case, we need to calculate the concentration of Ca2+ and SO42- in the solution. To do that, we will need to convert the given mass of CaSO4 to moles and then determine the concentrations using the given volume of water.
1. Convert mass of CaSO4 to moles:
Given: mass of CaSO4 = 1.9 g
Molar mass (MM) of CaSO4 = 136 g/mol
Moles = mass / molar mass
Moles = 1.9 g / 136 g/mol
Moles = 0.014 moles
2. Calculate the concentration (in mol/L) of Ca2+ (aq) and SO42- (aq):
Given: volume of water = 2.00 L
Concentration (Molarity) = moles / volume
Concentration of Ca2+ (aq) = 0.014 moles / 2.00 L = 0.007 M
Concentration of SO42- (aq) = 0.014 moles / 2.00 L = 0.007 M
3. Calculate the equilibrium constant (K) using the concentrations:
K = [Ca2+] * [SO42-]
K = (0.007 M) * (0.007 M) = 4.9 x 10^-5
Therefore, the equilibrium constant (K) for the given reaction is 4.9 x 10^-5.