What is the H⁺ concentration in a 0.05 M HCN solution given its Kₐ value?

The H⁺ concentration in 0.05 M HCN is approximately 5.0 × 10⁻⁴ M.

How do you calculate the H⁺ concentration in a weak acid like HCN?

Use the acid dissociation constant expression, setting up an equilibrium table to solve for [H⁺], considering the initial concentration and Kₐ.

Given that Kₐ for HCN is 5.0 × 10⁻¹⁰, what is the approximate H⁺ concentration in 0.05 M HCN?

The H⁺ concentration is approximately 5.0 × 10⁻⁴ M.

Why is the H⁺ concentration in HCN much lower than the initial concentration?

Because HCN is a weak acid with a small Kₐ value, it only partially dissociates, resulting in a low H⁺ concentration.

Can the H⁺ concentration in 0.05 M HCN be approximated directly from Kₐ?

Yes, since Kₐ is small, the H⁺ concentration can be approximated as the square root of (Kₐ × initial concentration), which yields about 5.0 × 10⁻⁴ M.

What is the significance of the Kₐ value being 5.0 × 10⁻¹⁰ for HCN?

It indicates that HCN is a very weak acid, dissociating very minimally in aqueous solution.

Is the H⁺ concentration in 0.05 M HCN affected significantly by the initial concentration?

Yes, for weak acids, the initial concentration influences the equilibrium H⁺ concentration, but due to low dissociation, the change is minimal.

How do you verify the H⁺ concentration calculation for HCN solution?

By applying the approximation [H⁺] ≈ √(Kₐ × initial concentration) and confirming that the assumption of negligible ionization of the initial concentration holds true.

What is the correct H(aq) concentration in 0.05 M HCN given Kₐ = 5.0 × 10⁻¹⁰?

The H⁺ concentration in the solution is approximately 5.0 × 10⁻⁴ M.

What Is The H(aq) Concentration In 0.05 M HCN(aq)? (K, For HCN Is 5.0 X 10-10) 5.0x10-10 M 5.0*10-4M

What Is The H(aq) Concentration In 0.05 M HCN(aq)? (K, For HCN Is 5.0 X 10-10) 5.0x10-10 M 5.010-4M

Understanding the concentration of hydrogen ions (H⁺ or H₃O⁺) in a solution of weak acid like hydrocyanic acid (HCN) is fundamental in chemistry, particularly in acid-base equilibria. Given a solution of 0.05 M HCN and the acid dissociation constant (Kₐ) of 5.0 × 10⁻¹⁰, determining the H⁺ concentration involves applying principles of equilibrium chemistry. The question also presents options—5.0 × 10⁻¹⁰ M and 5.0 × 10⁻⁴ M—prompting an analysis to identify the correct value based on the chemical properties and the mathematical approach involving the acid dissociation constant.

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Understanding Acid Dissociation Constant (Kₐ)

What Is Kₐ?

The acid dissociation constant, denoted as Kₐ, measures the strength of an acid in solution.
It is defined as the equilibrium constant for the dissociation of a weak acid (HA) into H⁺ and A⁻:

HA ⇌ H⁺ + A⁻

Mathematically, Kₐ = [H⁺][A⁻] / [HA]

The Significance of Kₐ Values

A small Kₐ (much less than 1) indicates a weak acid, which dissociates minimally.
Conversely, a large Kₐ (close to 1 or greater) suggests a strong acid, which dissociates extensively.

In our case, HCN has a Kₐ of 5.0 × 10⁻¹⁰, illustrating its weakness as an acid.

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Analyzing the Problem: HCN Dissociation in Water

Given Data

Initial concentration of HCN: [HCN]₀ = 0.05 M
Kₐ of HCN: 5.0 × 10⁻¹⁰
Unknown: [H⁺] (or [H₃O⁺]) at equilibrium

Assumptions for Weak Acid Calculations

The initial concentration of HCN is significantly larger than the concentration of H⁺ produced.
The degree of dissociation is small, allowing us to use the approximation that [HCN] ≈ [HCN]₀.

Setting Up the Equilibrium Expression

Let x = [H⁺] at equilibrium. Because HCN dissociates into H⁺ and CN⁻:

[H⁺] = x
[CN⁻] = x
[HCN] at equilibrium = [HCN]₀ - x ≈ [HCN]₀ (since x is small)

The equilibrium expression:

Kₐ = x² / ([HCN]₀ - x) ≈ x² / [HCN]₀

Rearranged:

x² = Kₐ × [HCN]₀

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Calculating the H⁺ Concentration

Applying the Approximation

Using the approximation that x ≪ [HCN]₀, the calculation simplifies:

x = √(Kₐ × [HCN]₀)

Substitute the known values:

x = √(5.0 × 10⁻¹⁰ × 0.05)

Calculate the product:

5.0 × 10⁻¹⁰ × 0.05 = 2.5 × 10⁻¹¹

Now, take the square root:

x = √(2.5 × 10⁻¹¹) ≈ √2.5 × 10⁻¹¹

√2.5 ≈ 1.58

Therefore:

x ≈ 1.58 × 10⁻⁶ M

Interpreting the Result

The equilibrium concentration of H⁺ ions is approximately 1.58 × 10⁻⁶ M.
This value is consistent with the expectation for a weak acid with such a small Kₐ.

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Comparison With Provided Options

5.0 × 10⁻¹⁰ M — This is roughly the Kₐ value itself, not the H⁺ concentration resulting from dissociation.
5.0 × 10⁻⁴ M — This is significantly larger than our calculated value and would suggest a much stronger acid or higher dissociation.

Given the calculation, the H⁺ concentration in 0.05 M HCN with a Kₐ of 5.0 × 10⁻¹⁰ is approximately 1.58 × 10⁻⁶ M, which is much closer to 10⁻⁶ than to either of the options provided.

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Understanding the Discrepancy in Options

Why Are the Options Confusing?

The options listed may be typographical or conceptual misinterpretations.
5.0 × 10⁻¹⁰ M corresponds to the Kₐ, representing the maximum possible H⁺ concentration if the acid dissociated completely, which it does not.
5.0 × 10⁻⁴ M suggests a much higher degree of dissociation than expected for such a weak acid.

Conclusion on Correct H⁺ Concentration

The accurate H⁺ concentration in 0.05 M HCN with a Kₐ of 5.0 × 10⁻¹⁰ is approximately 1.6 × 10⁻⁶ M.
Neither of the options provided exactly matches this value, but based on typical question structures, the closest conceptual answer is that the actual H⁺ concentration is very low, on the order of 10⁻⁶ M.

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The Importance of Accurate Calculations in Acid-Base Chemistry

Why Precision Matters

Small differences in Kₐ lead to large variations in pH calculations.
Correct assumptions (e.g., negligible dissociation) are critical for reliable results.

Practical Applications

Acid strength assessments.
Buffer solution preparations.
pH calculations in environmental and biological systems.

Summary and Final Remarks

The dissociation of HCN in water is minimal due to its very small Kₐ.
The H⁺ concentration in a 0.05 M HCN solution is approximately 1.6 × 10⁻⁶ M, confirming its status as a weak acid.
The options given (5.0 × 10⁻¹⁰ M and 5.0 × 10⁻⁴ M) do not precisely match the calculated value, but understanding the underlying principles clarifies that the actual concentration is closer to the former, very low value.

In conclusion, accurate application of equilibrium principles reveals that the hydrogen ion concentration in a 0.05 M HCN solution with a Kₐ of 5.0 × 10⁻¹⁰ is approximately 1.6 × 10⁻⁶ M, emphasizing the weak acidic nature of HCN and the importance of precise calculations in chemical equilibria.