- If 87 grams of K2SO4 (molar mass 174 grams) is dissolved in enough water to make 250 mL of solution, what are the concentrations of the potassium and the sulfate ions?
[K]
[SO42] - If 87 grams of Kä, SO4 (molar mass 174 grams) is dissolved in enough water to
(A)
0.020 M
0.020 M
(B)
1.0 M
2.0 M
(C)
2.0 M
1.0 M
(D)
2.0 M
2.0 M
(E)
4.0 M
2.0 M
The Correct Answer and Explanation is :
To calculate the concentrations of potassium ions (K⁺) and sulfate ions (SO₄²⁻), we need to follow these steps:
Step 1: Calculate the moles of K₂SO₄
We are given the mass of K₂SO₄, which is 87 grams, and its molar mass, which is 174 grams per mole. Using this information, we can calculate the number of moles of K₂SO₄ using the formula:
[
\text{Moles of K₂SO₄} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{87 \, \text{g}}{174 \, \text{g/mol}} = 0.5 \, \text{mol}
]
Step 2: Find the molarity of K₂SO₄
The volume of the solution is 250 mL, which is 0.250 L. The molarity (M) is calculated as:
[
\text{Molarity of K₂SO₄} = \frac{\text{Moles of K₂SO₄}}{\text{Volume of solution in L}} = \frac{0.5 \, \text{mol}}{0.250 \, \text{L}} = 2.0 \, \text{M}
]
Step 3: Determine the concentration of potassium ions (K⁺)
In each formula unit of K₂SO₄, there are two potassium ions (K⁺). Therefore, the concentration of K⁺ will be twice the molarity of K₂SO₄:
[
[\text{K}^+] = 2 \times 2.0 \, \text{M} = 4.0 \, \text{M}
]
Step 4: Determine the concentration of sulfate ions (SO₄²⁻)
Each formula unit of K₂SO₄ also contains one sulfate ion (SO₄²⁻), so the concentration of sulfate ions will be the same as the molarity of K₂SO₄:
[
[\text{SO₄}²⁻] = 2.0 \, \text{M}
]
Final Answer:
The concentrations are:
- Potassium ion concentration: 4.0 M
- Sulfate ion concentration: 2.0 M
Thus, the correct answer is (E):
- [K⁺] = 4.0 M
- [SO₄²⁻] = 2.0 M
I will also generate an image to visualize the steps involved.
Here is a visual representation of the calculation for the ion concentrations in the solution. It shows the steps for determining the moles, molarity, and final concentrations of potassium and sulfate ions in K₂SO₄. Let me know if you need further explanations or details!
