Sodium chloride is added to water (at 25⁰C) until it is saturated. Calculate the Cl- concentration in such a solution. Useful data are provided below.

∆G⁰f (kJ/mole): NaCl (s) -384
Na+ (aq) -262 Cl- (aq) -131

To calculate the Cl- concentration in a saturated solution of sodium chloride in water, we can use the Gibbs free energy of formation (∆G⁰f) values given for various species involved. The Gibbs free energy change (∆G) can be related to equilibrium constants (K) using the equation:

∆G = -RT ln(K)

Where:
R = Gas constant = 8.314 J/(mol·K)
T = Temperature in Kelvin
K = Equilibrium constant

In this case, we are interested in the equilibrium constant for the dissolution of NaCl in water, which can be expressed as:

NaCl (s) ⇌ Na+ (aq) + Cl- (aq)

Since we want to calculate the Cl- concentration, let's focus on the equilibrium constant expression for the dissociation of Cl-:

K = [Cl-]/[NaCl]

To calculate the Cl- concentration, we need to determine the ratio [Cl-]/[NaCl]. To do this, we can use the equation:

∆G⁰ = ∆G⁰f (products) - ∆G⁰f (reactants)

Here's how we can calculate the Cl- concentration:

1. Calculate ∆G⁰ for the dissociation of NaCl (s) into Na+ (aq) + Cl- (aq):
∆G⁰ = ∆G⁰f (Na+) + ∆G⁰f (Cl-) - ∆G⁰f (NaCl)
∆G⁰ = -262 kJ/mol + (-131 kJ/mol) - (-384 kJ/mol)
∆G⁰ = -262 kJ/mol + 131 kJ/mol - (-384 kJ/mol)
∆G⁰ = -262 kJ/mol + 131 kJ/mol + 384 kJ/mol
∆G⁰ = 253 kJ/mol

2. Convert the temperature from Celsius to Kelvin:
T = 25⁰C + 273.15 = 298.15 K

3. Use the ∆G = -RT ln(K) equation to solve for K:
-∆G⁰ = RT ln(K)
ln(K) = -∆G⁰ / (RT)
K = e^(-∆G⁰ / (RT))

4. Plug in the values into the equation and solve for K:
K = e^(-253 kJ/mol / (8.314 J/(mol·K) * 298.15 K))

K ≈ 3.06 x 10^13 (approximately)

5. Calculate the ratio [Cl-]/[NaCl] using the equilibrium expression:
K = [Cl-]/[NaCl]
[Cl-]/[NaCl] = K
[Cl-]/1 = 3.06 x 10^13

Therefore, the Cl- concentration in the saturated solution is approximately 3.06 x 10^13 M.