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Chapter 4: Problem 144

Use the following definition. In chemistry, the \(\mathrm{pH}\) of a solution is defined to be $$\mathrm{pH}=-\log \left[H^{+}\right],$$ where \(H^{+}\) is the hydrogen ion concentration of the solution in moles per liter. Distilled water has a pH of approximately 7. A substance with a pH under 7 is called an acid, and one with a pH over 7 is called a base. A healthy body maintains the hydrogen ion concentration of human blood at \(10^{-7.4}\) moles per liter. What is the pH of normal healthy blood? The condition of low blood \(\mathrm{pH}\) is called acidosis. Its symptoms are sickly sweet breath, headache, and nausea.

Short Answer

Expert verified
The pH of normal healthy blood is 7.4.

Step by step solution

01

Review the pH definition

Recall that the pH of a solution is defined by the formula \( \text{pH} = -\text{log} [H^+] \). This means that the pH value is the negative logarithm of the hydrogen ion concentration.
02

Identify the given hydrogen ion concentration

The problem states that the hydrogen ion concentration of normal healthy blood is \( 10^{-7.4} \) moles per liter.
03

Substitute the given value into the pH formula

Replace \( [H^+] \) in the formula with \( 10^{-7.4} \). So, we have \( \text{pH} = -\text{log} (10^{-7.4}) \).
04

Apply the logarithm rule

Use the logarithmic identity: \( \text{log} (10^x) = x \). Therefore, \( \text{log} (10^{-7.4}) = -7.4 \).
05

Simplify the expression

Substitute the result from the logarithm identity into the pH expression: \( \text{pH} = -(-7.4) \).
06

Calculate the pH value

Simplify \( -(-7.4) \) which results in \( \text{pH} = 7.4 \).

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Key Concepts

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

logarithms
Logarithms are mathematical operations that help us solve equations involving exponentials. They are the opposite, or inverse, of exponentiation. For example, if we have an equation like \(10^x = y\), we can find \(x\) by using the logarithm: \(x = \log_{10}(y)\). The base-10 logarithm, often written as 'log', is especially useful in chemistry. This is because many chemical concentrations are expressed in powers of ten, making logs a practical tool. Understanding logarithms is crucial when calculating pH values, as pH is defined using the negative base-10 logarithm of the hydrogen ion concentration.
hydrogen ion concentration
The hydrogen ion concentration, written as \([H^+]\), is a measure of the number of hydrogen ions in a solution. It's crucial in determining the solution's acidity or basicity. In moles per liter (mol/L), the concentration tells us how many moles of hydrogen ions are in one liter of solution. For instance, a concentration of \(10^{-7.4}\) mol/L means there are \(10^{-7.4}\) moles of hydrogen ions per liter of blood. By knowing the \([H^+]\), we can use the pH formula to determine if the solution is acidic, neutral, or basic.
acid-base chemistry
Acid-base chemistry explores the balance between acids and bases in substances. Acids have a pH less than 7, while bases have a pH greater than 7. pH, which stands for 'potential of Hydrogen', gauges the acidity or basicity of a solution based on its hydrogen ion concentration. Human blood is slightly basic with a pH around 7.4. Maintaining this balance is critical for bodily functions. When the pH balance shifts, conditions like acidosis (low pH) or alkalosis (high pH) can occur, affecting health negatively.
moles per liter
Moles per liter (mol/L) is a common unit used in chemistry to express the concentration of a substance in a solution. One mole is an amount of a substance that contains as many entities (atoms, molecules) as there are in 12 grams of carbon-12. So, when we talk about hydrogen ion concentration in mol/L, we relate it to how many moles of hydrogen ions are in one liter of solution. For example, healthy blood has a hydrogen ion concentration of \(10^{-7.4}\) mol/L, meaning there are \(10^{-7.4}\) moles of \(H^+\) per liter of blood. Understanding this measurement helps us use the pH formula accurately.

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