Calculate the pH at $25^{\circ} C$ of a 0.68 M solution of sodium propionate $\left( NaC _2 H _5 CO _2\right)$. Note that propionic acid $\left( HC _2 H _5 CO _2\right)$ is a weak acid with a $p K_a$ of 4.89. Round your answer to 1 decimal place.
$pH=$
Answer (1)
Calculate p K b using p K b = 14 − p K a = 14 − 4.89 = 9.11 .
Calculate K b using K b = 1 0 − p K b = 1 0 − 9.11 .
Set up the equilibrium expression K b = 0.68 x 2 and solve for x , where x = [ O H − ] .
Calculate pO H = − lo g [ O H − ] and then p H = 14 − pO H . The final answer is 9.4 .
Explanation
Problem Analysis We are given a 0.68 M solution of sodium propionate ( N a C 2 H 5 C O 2 ), which is the salt of a weak acid, propionic acid ( H C 2 H 5 C O 2 ). The p K a of propionic acid is 4.89. We need to find the pH of this solution at 2 5 ∘ C . Since sodium propionate is the salt of a weak acid, it will undergo hydrolysis in water, producing O H − ions, which will make the solution basic.
Calculating p K b First, we need to find the p K b of the propionate ion ( C 2 H 5 C O 2 − ). We know that p K a + p K b = 14 . Therefore, p K b = 14 − p K a = 14 − 4.89 = 9.11 .
Calculating K b Next, we calculate K b from p K b using the formula K b = 1 0 − p K b . So, K b = 1 0 − 9.11 .
Setting up the ICE table Now, we set up an ICE table for the hydrolysis of the propionate ion in water:
C 2 H 5 C O 2 − + H 2 O ⇌ H C 2 H 5 C O 2 + O H −
Initial: 0.68 M 0 0 Change: -x +x +x Equilibrium: 0.68 - x x x
K b = [ C 2 H 5 C O 2 − ] [ H C 2 H 5 C O 2 ] [ O H − ] = 0.68 − x x 2
Approximation and Solving for x Since K b is small, we can assume that x << 0.68 , so 0.68 − x ≈ 0.68 . Then, K b = 0.68 x 2 . Solving for x:
x = K b ∗ 0.68 = 1 0 − 9.11 ∗ 0.68
Calculating pO H Now, we calculate the pO H using the formula pO H = − l o g [ O H − ] = − l o g ( x ) .
Calculating p H Finally, we calculate the p H using the formula p H = 14 − pO H . The result of the calculation is 9.4.
Final Answer Therefore, the pH of the 0.68 M solution of sodium propionate is 9.4.
Examples
Understanding pH is crucial in many real-world applications. For instance, in agriculture, knowing the pH of the soil helps farmers determine the best crops to grow and the right fertilizers to use. In medicine, maintaining the correct pH balance in our blood is vital for our health. Similarly, in environmental science, monitoring the pH of water bodies helps assess pollution levels and protect aquatic life. The pH calculation of a salt solution, like sodium propionate, demonstrates how chemical principles are applied in various scientific fields.
