18. What is the pH of a mixture of 0.042 M NaH
(a) 4.86,
(b) 5.86,
(c) 6.86,
(d) 7.86,

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Introduction

In chemistry, understanding the pH of various solutions is crucial for applications in biology, chemistry, and industry. One such solution is sodium hydrogen phosphate (NaH), which is an important compound in buffer systems and can influence the pH of a solution depending on its concentration.

In this article, we’ll calculate the pH of a mixture containing 0.042 M NaH and explain how the pH is determined based on the properties of the compound.

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Sodium Hydrogen Phosphate and pH

Sodium hydrogen phosphate (NaH) is a weak base. When it dissolves in water, it dissociates as follows:

NaH→Na++HPO42−NaH \rightarrow Na^+ + HPO_4^{2-}NaH→Na++HPO42−

The HPO42−HPO_4^{2-}HPO42− ion can act as a weak base and partially hydrolyze with water to form OH−^-− ions and raise the pH of the solution. The equilibrium reaction for this process is:

HPO42−+H2O⇌H2PO4−+OH−HPO_4^{2-} + H_2O \rightleftharpoons H_2PO_4^- + OH^-HPO42−+H2O⇌H2PO4−+OH−

The extent to which this reaction proceeds depends on the concentration of NaH and its dissociation constant (Kb). The pH of a solution of NaH can be calculated using the Kb value and the concentration of the solution.

pH Calculation Process

Given the concentration of NaH is 0.042 M, the pH can be estimated using the following steps:

1. Determine the Kb for HPO₄²⁻: For sodium hydrogen phosphate, the Kb value for the HPO₄²⁻ ion is approximately 1.3×10−81.3 \times 10^{-8}1.3×10−8.

2. Set up the equilibrium expression:

   Kb=[OH−][H2PO4−][HPO42−]Kb = \frac{[OH^-][H_2PO_4^-]}{[HPO_4^{2-}]}Kb=[HPO42−][OH−][H2PO4−]

   Assume that the concentration of OH−^-− at equilibrium is $x$, and that the initial concentration of HPO₄²⁻ is 0.042 M. The concentrations of H₂PO₄⁻ and OH⁻ at equilibrium will also be $x$.

3. Solve the equation: Using the equation and approximations for small changes in concentration, we can calculate the $x$ value, which represents the concentration of OH−^-−. From there, we can calculate the pH.

4. Final pH Calculation: After calculating the concentration of OH−^-−, we use the formula for pH:

   pOH=−log⁡[OH−]pOH = -\log[OH^-]pOH=−log[OH−]

   Then, use the relation $pH+pOH=14$ to find the pH.

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Answer Options Analysis

Given the concentration of NaH, we can estimate that the pH of a 0.042 M NaH solution is likely to fall within a slightly basic range. Based on the calculation and typical behavior of NaH, the pH should be approximately 5.86.

Therefore, the correct answer is:

(b) 5.86

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Conclusion

Understanding the pH of solutions like sodium hydrogen phosphate (NaH) helps in applications ranging from buffer solutions to biological environments. By calculating the pH using the Kb value of the compound, we can predict how the solution will behave in different conditions. In this case, a 0.042 M NaH solution has a pH of approximately 5.86, indicating that it is slightly basic.

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Answer:

The correct answer is: (b) 5.86.