The pH of a solution in which [OH-]=3.1×10^-4M
The correct answer and explanation is :
Alright, let’s dive into this carefully:
First, to find the pH from a given hydroxide ion concentration ([OH^-]), we use the following steps:
- Find the pOH using the formula:
[
\text{pOH} = -\log [\text{OH}^-]
] - Find the pH using the relation:
[
\text{pH} + \text{pOH} = 14
]
Given:
[
[\text{OH}^-] = 3.1 \times 10^{-4} \, \text{M}
]
First, calculate the pOH:
[
\text{pOH} = -\log (3.1 \times 10^{-4})
]
Using log rules:
[
\log (3.1 \times 10^{-4}) = \log(3.1) + \log(10^{-4})
]
[
= \log(3.1) – 4
]
[
\log(3.1) \approx 0.491
]
Thus,
[
\text{pOH} = -(0.491 – 4) = 3.509
]
Now, use the relationship between pH and pOH:
[
\text{pH} = 14 – \text{pOH}
]
[
\text{pH} = 14 – 3.509
]
[
\text{pH} = 10.491
]
Thus, the pH is approximately 10.49.
300-word explanation
Understanding the pH of a solution is crucial in chemistry as it tells us how acidic or basic a solution is. In this question, we were given the concentration of hydroxide ions, ([OH^-]), which directly relates to the basicity of the solution.
The pOH is the negative logarithm (base 10) of the hydroxide ion concentration. The “p” in pOH or pH stands for “power,” reflecting the exponent in the scientific notation of the concentration. Calculating the pOH first is necessary because the relationship between pH and pOH is straightforward: their sum is always 14 at 25°C. This relationship is derived from the ion-product constant for water, (K_w = [H^+][OH^-] = 1.0 \times 10^{-14}).
In this case, we took the ([OH^-]) concentration, (3.1 \times 10^{-4}), and found its negative logarithm to get the pOH, which turned out to be approximately 3.509. Afterward, we used the key formula ( \text{pH} + \text{pOH} = 14 ) to solve for pH, resulting in a pH of about 10.49.
Since the pH is greater than 7, the solution is basic, which makes sense given the high ([OH^-]) concentration. Generally, pH values below 7 indicate acidity, a pH of 7 is neutral (like pure water), and pH values above 7 show basicity.
This process is fundamental in fields like biochemistry, environmental science, and medicine, where the pH of solutions can influence chemical reactions, biological activity, and environmental conditions.