The PH Of Lemon Juice At 298 K Is Found To Be 2.32. What Is The Concentration Of $H_3O^{+}$ Ions In The Solution?Use $\left[ H_3O {+}\right]=10 {-pH}$.A. 1.05 × 10 − 3 M 1.05 \times 10^{-3} \, \text{M} 1.05 × 1 0 − 3 M B. $4.79 \times 10^{-3} ,

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Understanding pH and H3O+ Ions

pH is a measure of the concentration of hydrogen ions (H+) in a solution. It is a crucial parameter in chemistry, as it determines the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with a pH of 7 being neutral. A pH below 7 indicates an acidic solution, while a pH above 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:

[H3O+]=10−pH\left[ H_3O^{+}\right]=10^{-pH}

This formula is derived from the Arrhenius definition of acid, which states that an acid is a substance that increases the concentration of hydrogen ions in a solution.

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.

[H3O+]=10−2.32\left[ H_3O^{+}\right]=10^{-2.32}

Calculating the Concentration

To calculate the concentration, we need to evaluate the expression 10−2.3210^{-2.32}. This can be done using a calculator or by using the properties of exponents.

10−2.32=1102.3210^{-2.32} = \frac{1}{10^{2.32}}

Evaluating the Exponent

To evaluate the exponent, we can use the fact that 10x=exln⁡1010^x = e^{x \ln 10}, where ee is the base of the natural logarithm and ln⁡10\ln 10 is the natural logarithm of 10.

102.32=e2.32ln⁡1010^{2.32} = e^{2.32 \ln 10}

Calculating the Value

Using a calculator, we can evaluate the expression e2.32ln⁡10e^{2.32 \ln 10} to get:

e2.32ln⁡10≈1.05×102e^{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 in the solution.

[H3O+]=11.05×102\left[ H_3O^{+}\right] = \frac{1}{1.05 \times 10^2}

Simplifying the Expression

To simplify the expression, we can divide 1 by 1.05×1021.05 \times 10^2 to get:

[H3O+]=9.52×10−3 M\left[ H_3O^{+}\right] = 9.52 \times 10^{-3} \, \text{M}

However, this is not the correct answer. Let's re-evaluate the expression.

Re-Evaluating the Expression

To re-evaluate the expression, we can use the fact that 10−x=110x10^{-x} = \frac{1}{10^x}.

[H3O+]=1102.32\left[ H_3O^{+}\right] = \frac{1}{10^{2.32}}

Evaluating the Exponent

To evaluate the exponent, we can use the fact that 10x=exln⁡1010^x = e^{x \ln 10}.

102.32=e2.32ln⁡1010^{2.32} = e^{2.32 \ln 10}

Calculating the Value

Using a calculator, we can evaluate the expression e2.32ln⁡10e^{2.32 \ln 10} to get:

e2.32ln⁡10≈1.05×102e^{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 in the solution.

[H3O+]=11.05×102\left[ H_3O^{+}\right] = \frac{1}{1.05 \times 10^2}

Simplifying the Expression

To simplify the expression, we can divide 1 by 1.05×1021.05 \times 10^2 to get:

[H3O+]=9.52×10−3 M\left[ H_3O^{+}\right] = 9.52 \times 10^{-3} \, \text{M}

However, this is not the correct answer. Let's re-evaluate the expression again.

Re-Evaluating the Expression Again

To re-evaluate the expression, we can use the fact that 10−x=110x10^{-x} = \frac{1}{10^x}.

[H3O+]=10−2.32\left[ H_3O^{+}\right] = 10^{-2.32}

Evaluating the Exponent

To evaluate the exponent, we can use the fact that 10x=exln⁡1010^x = e^{x \ln 10}.

10−2.32=e−2.32ln⁡1010^{-2.32} = e^{-2.32 \ln 10}

Calculating the Value

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

e−2.32ln⁡10≈4.79×10−3e^{-2.32 \ln 10} \approx 4.79 \times 10^{-3}

Calculating the Concentration

Now that we have evaluated the exponent, we can calculate the concentration of H3O+ ions in the solution.

[H3O+]=4.79×10−3 M\left[ H_3O^{+}\right] = 4.79 \times 10^{-3} \, \text{M}

The final answer is: 4.79×10−3\boxed{4.79 \times 10^{-3}}

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 a crucial parameter in chemistry, as it determines the acidity or basicity of a solution. The pH scale ranges from 0 to 14, with a pH of 7 being neutral. A pH below 7 indicates an acidic solution, while a pH above 7 indicates a basic solution. The concentration of H3O+ ions in a solution can be calculated using the formula: $\left[ H_3O{+}\right]=10{-pH}$

Q: What is the pH of lemon juice and how can we calculate the concentration of H3O+ ions in it?

A: The pH of lemon juice at 298 K is 2.32. We can use the formula $\left[ H_3O{+}\right]=10{-pH}$ to calculate the concentration of H3O+ ions in the solution.

Q: How do we calculate the concentration of H3O+ ions in a solution using the formula?

A: To calculate the concentration of H3O+ ions in a solution using the formula, we need to evaluate the expression 10−pH10^{-pH}. This can be done using a calculator or by using the properties of exponents.

Q: What is the correct answer for the concentration of H3O+ ions in lemon juice?

A: The correct answer for the concentration of H3O+ ions in lemon juice is 4.79×10−3 M4.79 \times 10^{-3} \, \text{M}.

Q: Why is it important to understand the pH of a solution and the concentration of H3O+ ions in it?

A: Understanding the pH of a solution and the concentration of H3O+ ions in it is crucial in various fields such as chemistry, biology, and medicine. It helps us to determine the acidity or basicity of a solution, which is essential in understanding various chemical reactions and processes.

Q: How can we use the formula to calculate the concentration of H3O+ ions in other solutions?

A: We can use the formula $\left[ H_3O{+}\right]=10{-pH}$ to calculate the concentration of H3O+ ions in other solutions by substituting the pH value of the solution into the formula.

Q: What are some common applications of pH and the concentration of H3O+ ions in real-life scenarios?

A: pH and the concentration of H3O+ ions have various applications in real-life scenarios such as:

  • Food industry: pH is used to determine the acidity or basicity of food products, which is essential in maintaining food safety and quality.
  • Water treatment: pH is used to determine the acidity or basicity of water, which is essential in maintaining water quality and safety.
  • Medical industry: pH is used to determine the acidity or basicity of bodily fluids, which is essential in diagnosing and treating various medical conditions.

Q: How can we measure the pH of a solution accurately?

A: We can measure the pH of a solution accurately using a pH meter or pH paper. A pH meter is a device that measures the pH of a solution by detecting the concentration of H3O+ ions in it. pH paper is a type of paper that changes color in response to the pH of a solution.

Q: What are some common mistakes to avoid when calculating the concentration of H3O+ ions in a solution?

A: Some common mistakes to avoid when calculating the concentration of H3O+ ions in a solution include:

  • Using the wrong formula or equation
  • Making errors in calculating the exponent
  • Not considering the units of the concentration
  • Not checking the accuracy of the pH value used in the calculation

Q: How can we ensure the accuracy of our calculations when determining the concentration of H3O+ ions in a solution?

A: We can ensure the accuracy of our calculations when determining the concentration of H3O+ ions in a solution by:

  • Using the correct formula and equation
  • Double-checking our calculations for errors
  • Considering the units of the concentration
  • Verifying the accuracy of the pH value used in the calculation

Q: What are some common applications of pH and the concentration of H3O+ ions in chemistry?

A: pH and the concentration of H3O+ ions have various applications in chemistry such as:

  • Determining the acidity or basicity of a solution
  • Understanding chemical reactions and processes
  • Determining the concentration of ions in a solution
  • Understanding the properties of acids and bases

Q: How can we use pH and the concentration of H3O+ ions to understand chemical reactions and processes?

A: We can use pH and the concentration of H3O+ ions to understand chemical reactions and processes by:

  • Determining the acidity or basicity of a solution
  • Understanding the properties of acids and bases
  • Determining the concentration of ions in a solution
  • Understanding the effects of pH on chemical reactions and processes