What is the pH of a 0.56 M solution of dimethylamine?
The correct answer and explanation is:
To determine the pH of a 0.56 M solution of dimethylamine (DMA), we need to understand its nature as a weak base and apply the equilibrium expression for its dissociation in water.
Dimethylamine is a weak base and will react with water in the following way: DMA+H2O⇌DMAH++OH−\text{DMA} + \text{H}_2\text{O} \rightleftharpoons \text{DMAH}^+ + \text{OH}^-
Here, DMA (dimethylamine) accepts a proton from water, forming DMAH+ (dimethylammonium ion) and hydroxide ions (OH-).
To calculate the pH, we first need the base dissociation constant (Kb) for dimethylamine. The Kb for dimethylamine is typically given as: Kb=5.4×10−4\text{Kb} = 5.4 \times 10^{-4}
Step 1: Set up the equilibrium expression
Using the formula for Kb: Kb=[DMAH+][OH−][DMA]\text{Kb} = \frac{[\text{DMAH}^+][\text{OH}^-]}{[\text{DMA}]}
At equilibrium, the concentration of DMAH+ and OH- will be equal, and the concentration of DMA will decrease by this amount.
Step 2: Set up the ICE table
| Species | Initial Concentration | Change in Concentration | Equilibrium Concentration |
|---|---|---|---|
| DMA | 0.56 M | -x | 0.56 – x |
| DMAH+ | 0 | +x | x |
| OH- | 0 | +x | x |
Step 3: Substitute into the Kb expression
Kb=x20.56−x\text{Kb} = \frac{x^2}{0.56 – x}
Since the Kb value is small, we can assume that xx is much smaller than 0.56, so we approximate 0.56−x≈0.560.56 – x \approx 0.56. 5.4×10−4=x20.565.4 \times 10^{-4} = \frac{x^2}{0.56}
Solving for xx (which represents [OH-]): x2=(5.4×10−4)(0.56)=3.024×10−4x^2 = (5.4 \times 10^{-4})(0.56) = 3.024 \times 10^{-4} x=3.024×10−4=0.0174 Mx = \sqrt{3.024 \times 10^{-4}} = 0.0174 \, \text{M}
So, the concentration of OH- is approximately 0.0174 M.
Step 4: Calculate the pOH
The pOH is given by: pOH=−log[OH−]\text{pOH} = -\log [\text{OH}^-]
Substitute the value of [OH-]: pOH=−log(0.0174)=1.76\text{pOH} = -\log(0.0174) = 1.76
Step 5: Calculate the pH
Finally, the pH can be found using the relationship: pH=14−pOH\text{pH} = 14 – \text{pOH} pH=14−1.76=12.24\text{pH} = 14 – 1.76 = 12.24
Thus, the pH of the 0.56 M solution of dimethylamine is approximately 12.24.