- Using the Ka’s for HC2H3O2 (1.8×10-5) and HCO3- (5.6×10-11) :
a) Calculate the Kb for C2H3O2-
b)Calculate the Kb for CO32-
- In order to prepare 50.0 mL of 0.200 M HCl you will addmL of 1.00 M HCI tomL of water.
The Correct Answer and Explanation is :
1. Calculating Kb for C₂H₃O₂⁻ and CO₃²⁻
To find the base dissociation constant (Kb) for the conjugate bases C₂H₃O₂⁻ (acetate) and CO₃²⁻ (carbonate), we use the relationship between Ka and Kb:
[
K_w = K_a \times K_b
]
where Kw (the ionization constant for water) is 1.0 × 10⁻¹⁴ at 25°C.
(a) Calculating Kb for C₂H₃O₂⁻
Given:
- Ka for HC₂H₃O₂ (acetic acid) = 1.8 × 10⁻⁵
- Kw = 1.0 × 10⁻¹⁴
[
K_b = \frac{K_w}{K_a}
]
[
K_b = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}}
]
[
K_b = 5.56 \times 10^{-10}
]
(b) Calculating Kb for CO₃²⁻
Given:
- Ka for HCO₃⁻ (bicarbonate) = 5.6 × 10⁻¹¹
- Kw = 1.0 × 10⁻¹⁴
[
K_b = \frac{K_w}{K_a}
]
[
K_b = \frac{1.0 \times 10^{-14}}{5.6 \times 10^{-11}}
]
[
K_b = 1.79 \times 10^{-4}
]
2. Preparing 50.0 mL of 0.200 M HCl from 1.00 M HCl
To dilute a stock solution, we use the dilution formula:
[
M_1V_1 = M_2V_2
]
where:
- M₁ = initial concentration (1.00 M),
- V₁ = volume of stock solution needed (mL),
- M₂ = final concentration (0.200 M),
- V₂ = final total volume (50.0 mL).
Solving for V₁:
[
V_1 = \frac{M_2 \times V_2}{M_1}
]
[
V_1 = \frac{(0.200 \text{ M}) (50.0 \text{ mL})}{1.00 \text{ M}}
]
[
V_1 = 10.0 \text{ mL}
]
Thus, you need 10.0 mL of 1.00 M HCl.
To get a total volume of 50.0 mL, the amount of water needed is:
[
V_{\text{water}} = V_2 – V_1
]
[
V_{\text{water}} = 50.0 \text{ mL} – 10.0 \text{ mL}
]
[
V_{\text{water}} = 40.0 \text{ mL}
]
Explanation
Dilution involves reducing the concentration of a solution by adding more solvent (water). Since M₁V₁ = M₂V₂ holds true, this ensures the number of moles of solute remains constant before and after dilution. Here, 10.0 mL of 1.00 M HCl contains the same number of moles as 50.0 mL of 0.200 M HCl but spread over a larger volume.
To prepare this solution correctly:
- Measure 10.0 mL of 1.00 M HCl using a pipette.
- Transfer it to a 50.0 mL volumetric flask or a graduated cylinder.
- Add distilled water until the total volume reaches 50.0 mL.
- Mix well to ensure uniformity.
It is important to add acid to water and not the other way around, as adding water to concentrated acid can cause heat release, leading to splashing or even dangerous reactions.