Applying the Formula to Lemon Juice

Oct 13, 2025 by thesweetdesigns.com 140 views

Understanding pH and H3O+ Ions

pH is a measure of the concentration of hydrogen ions (H+) in a solution. It is defined as the negative logarithm of the concentration of H+ ions. The pH scale ranges from 0 to 14, with a pH of 7 being neutral (neither acidic nor basic). A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution.

Calculating the Concentration of H3O+ Ions

The concentration of H3O+ ions in a solution can be calculated using the formula:

\left[ H_3O^+ \right] = 10^{- \text{pH}}

This formula is derived from the definition of pH, which is the negative logarithm of the concentration of H+ ions.

Applying the Formula to Lemon Juice

Given that the pH of lemon juice at 298 K is 2.32, we can use the formula to calculate the concentration of H3O+ ions in the solution.

\left[ H_3O^+ \right] = 10^{- 2.32}

Calculating the Concentration

To calculate the concentration of H3O+ ions, we need to evaluate the expression $10^{- 2.32}$ . This can be done using a calculator or by using the properties of exponents.

10^{- 2.32} = \frac{1}{10^{2.32}}

Evaluating the Exponent

To evaluate the exponent, we can use the fact that $10^x = e^{x \ln 10}$ , where $e$ is the base of the natural logarithm and $\ln 10$ is the natural logarithm of 10.

10^{2.32} = e^{2.32 \ln 10}

Calculating the Value

Using a calculator, we can evaluate the expression $e^{2.32 \ln 10}$ to get:

e^{2.32 \ln 10} \approx 1.05 \times 10^2

Calculating the Concentration

Now that we have evaluated the exponent, we can calculate the concentration of H3O+ ions:

\left[ H_3O^+ \right] = \frac{1}{1.05 \times 10^2}

Simplifying the Expression

To simplify the expression, we can divide 1 by $1.05 \times 10^2$ :

\left[ H_3O^+ \right] = \frac{1}{1.05 \times 10^2} = \frac{1}{105}

Converting to Scientific Notation

To express the concentration in scientific notation, we can write:

\left[ H_3O^+ \right] = 9.52 \times 10^{-3}

Conclusion

The concentration of H3O+ ions in lemon juice at 298 K is $9.52 \times 10^{-3} M$ . This is a relatively high concentration of H+ ions, indicating that lemon juice is a strong acid.

Answer

The correct answer is:

\boxed{9.52 \times 10^{-3} M}

However, the options provided are:

A. $$1.05 \times 10^{-3} , M$$

B. $$4.79 \times 10^{-3} , M$$

C. $$9.52 \times 10^{-3} , M$$

D. $$1.05 \times 10^{-2} , M$$

The closest answer is:

C. $$9.52 \times 10^{-3} , M$$

Frequently Asked Questions

Q: What is pH and how is it related to the concentration of H3O+ ions?

A: pH is a measure of the concentration of hydrogen ions (H+) in a solution. It is defined as the negative logarithm of the concentration of H+ ions. The pH scale ranges from 0 to 14, with a pH of 7 being neutral (neither acidic nor basic). A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution.

Q: How is the concentration of H3O+ ions calculated?

A: The concentration of H3O+ ions in a solution can be calculated using the formula:

\left[ H_3O^+ \right] = 10^{- \text{pH}}

This formula is derived from the definition of pH, which is the negative logarithm of the concentration of H+ ions.

Q: What is the pH of lemon juice and how is it related to the concentration of H3O+ ions?

A: The pH of lemon juice at 298 K is 2.32. Using the formula, we can calculate the concentration of H3O+ ions in the solution:

\left[ H_3O^+ \right] = 10^{- 2.32}

Q: How do I calculate the concentration of H3O+ ions in a solution?

A: To calculate the concentration of H3O+ ions, you need to evaluate the expression $10^{- \text{pH}}$ . This can be done using a calculator or by using the properties of exponents.

Q: What is the concentration of H3O+ ions in lemon juice at 298 K?

A: The concentration of H3O+ ions in lemon juice at 298 K is $9.52 \times 10^{-3} M$ . This is a relatively high concentration of H+ ions, indicating that lemon juice is a strong acid.

Q: How do I express the concentration of H3O+ ions in scientific notation?

A: To express the concentration in scientific notation, you can write:

\left[ H_3O^+ \right] = 9.52 \times 10^{-3}

Q: What is the relationship between pH and the concentration of H3O+ ions?

A: The pH of a solution is directly related to the concentration of H3O+ ions. A lower pH indicates a higher concentration of H+ ions, while a higher pH indicates a lower concentration of H+ ions.

Q: Can I use the formula to calculate the pH of a solution?

A: Yes, you can use the formula to calculate the pH of a solution. The formula is:

\text{pH} = - \log \left[ H_3O^+ \right]

This formula is the inverse of the formula for calculating the concentration of H3O+ ions.

Q: What is the significance of the pH of lemon juice?

A: The pH of lemon juice is significant because it indicates the acidity of the solution. A pH of 2.32 indicates that lemon juice is a strong acid and can potentially damage surfaces or harm living organisms.

Q: Can I use lemon juice as a cleaning agent?

A: Yes, you can use lemon juice as a cleaning agent due to its acidity. However, be careful not to use it on surfaces that may be damaged by the acidity.

Q: What are some common applications of pH in everyday life?

A: pH is used in a variety of applications, including:

Cleaning and disinfecting surfaces
Preserving food and drinks
Testing the acidity of soil and water
Developing new products and materials

Q: How can I measure the pH of a solution?

A: You can measure the pH of a solution using a pH meter or pH paper. A pH meter is a device that measures the pH of a solution directly, while pH paper is a strip that changes color depending on the pH of the solution.

Q: What are some common mistakes to avoid when working with pH?

A: Some common mistakes to avoid when working with pH include:

Not calibrating the pH meter properly
Not using the correct pH paper or pH meter for the solution being tested
Not taking into account the temperature of the solution when measuring pH
Not following proper safety protocols when handling acidic or basic solutions.