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Chapter 4: Problem 143

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. The hydrogen ion concentration of orange juice is \(10^{-3.7}\) moles per liter. Find the pH of orange juice.

Short Answer

Expert verified
The pH of orange juice is 3.7, making it an acid.

Step by step solution

01

Identify the formula and given values

The formula to calculate pH is given by \( \mathrm{pH} = -\log \, [H^{+}] \). The hydrogen ion concentration of orange juice \([H^{+}]\) is given as \(10^{-3.7}\) moles per liter.
02

Plug the given value into the formula

Substitute \([H^{+}]\) with \(10^{-3.7}\) in the pH formula: \( \mathrm{pH} = -\log \, (10^{-3.7}) \).
03

Apply the logarithm properties

Utilize the property of logarithms that \( \log(10^{x}) = x \). Thus, \( \log(10^{-3.7}) = -3.7 \).
04

Simplify the expression

Simplify the pH formula: \( \mathrm{pH} = -(-3.7) = 3.7 \).
05

Conclusion

Therefore, the pH of orange juice is 3.7. Since this pH value is less than 7, it classifies orange juice as an acid.

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Key Concepts

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

Logarithm Properties
Understanding the properties of logarithms is crucial for solving pH calculations in chemistry. One important property is that the logarithm of a power of 10 can be simplified easily. For example, the logarithm of 10 raised to the power of any number, say x, is simply that number x. Mathematically, this is expressed as \( \log(10^{x}) = x \).

This property helps to simplify the expression when calculating pH. In our exercise, we use this property to simplify the expression \( \log(10^{-3.7}) \), which becomes \ -3.7 \. Doing so makes it straightforward to find the pH of various solutions by using their hydrogen ion concentration directly.

Additionally, the negative sign in the pH formula (\

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