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Chapter 10: Problem 37

Find the \(\mathrm{pH}\) (to the nearest tenth) of the substance with the given hydronium ion concentration. $$ \text { Ammonia, } 2.5 \times 10^{-12} $$

Short Answer

Expert verified
The \(\text{pH}\) is approximately 11.6.

Step by step solution

01

Identify the formula for pH calculation

The \(\text{pH}\) of a substance can be calculated using the formula: \[ \text{pH} = -\text{log} \left[\text{H}_3\text{O}^+\right] \] where \[ \left[\text{H}_3\text{O}^+\right] \] is the hydronium ion concentration.
02

Substitute the given hydronium ion concentration

Substitute \[ \left[\text{H}_3\text{O}^+\right] = 2.5 \times 10^{-12} \] into the formula.
03

Calculate the pH

Evaluate the expression: \[ \text{pH} = -\text{log} \left(2.5 \times 10^{-12}\right) \] Use a calculator to find the approximate pH value.
04

Round to the nearest tenth

After calculating, round the \(\text{pH}\) value to the nearest tenth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hydronium Ion Concentration
Hydronium ion concentration refers to the amount of hydronium ions \(\text{H}_3\text{O}^+\) present in a solution. It is often used to determine the acidity or basicity of a solution. In aqueous solutions, acids increase the concentration of \[ \text{H}_3\text{O}^+ \].
Logarithmic Functions
Logarithmic functions are the inverse of exponential functions. In this context, we use the logarithm to determine the \(\text{pH}\) of a substance. The formula we use is \[ \text{pH} = -\text{log} \left[ \text{H}_3\text{O}^+ \right] \]. This means that we need to calculate the negative logarithm (base 10) of the hydronium ion concentration.
Rounding Numbers
Once we calculate the \(\text{pH}\), we typically need to round the result for easier communication. Rounding to the nearest tenth means if the hundredths place is 5 or more, you round up the tenths place by 1. Otherwise, you keep the tenths place as it is.

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Most popular questions from this chapter

Graph each logarithmic function. $$f(x)=\log _{1 / 5} x$$

Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places. $$ \log _{3} \sqrt{2} $$

To four decimal places, the values of \(\log _{10} 2\) and \(\log _{10} 9\) are $$\log _{10} 2=0.3010 \text { and } \log _{10} 9=0.9542$$ Use these values and the properties of logarithms to evaluate each expression. DO NOT USE A CALCULATOR. See Example 5. $$ \log _{10} 162 $$

Solve each equation. Approximate solutions to three decimal places. $$ 3^{2 x}=14 $$

Use the special properties of logarithms to evaluate each expression. $$\log _{6} \frac{1}{6}$$
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