How many grams of potassium permanganate, KMnO4, are present in 125 mL of a 0.0850 M solution?
The correct answer and explanation is :
To find the mass of potassium permanganate (KMnO₄) in a 125 mL solution with a molarity of 0.0850 M, we can follow these steps:
Step 1: Convert the volume of the solution to liters
Molarity (M) is defined as the number of moles of solute per liter of solution. The given volume is 125 mL, but we need it in liters to use it in the formula for molarity.
$$
\text{Volume (in liters)} = \frac{125 \, \text{mL}}{1000} = 0.125 \, \text{L}
$$
Step 2: Calculate the moles of KMnO₄
Using the formula for molarity, which is:
$$
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution (in L)}}
$$
We can rearrange this to find the moles of KMnO₄:
$$
\text{moles of KMnO₄} = \text{Molarity} \times \text{Volume (in L)}
$$
Substitute the given values:
$$
\text{moles of KMnO₄} = 0.0850 \, \text{M} \times 0.125 \, \text{L} = 0.010625 \, \text{moles of KMnO₄}
$$
Step 3: Convert moles of KMnO₄ to grams
Now, we need to convert the moles of KMnO₄ to grams. To do this, we use the molar mass of KMnO₄. The molar mass of KMnO₄ is calculated by adding the atomic masses of each element:
- Potassium (K): 39.10 g/mol
- Manganese (Mn): 54.94 g/mol
- Oxygen (O): 16.00 g/mol (4 atoms of oxygen)
$$
\text{Molar mass of KMnO₄} = 39.10 \, \text{g/mol} + 54.94 \, \text{g/mol} + (4 \times 16.00 \, \text{g/mol}) = 158.04 \, \text{g/mol}
$$
Next, multiply the number of moles by the molar mass:
$$
\text{mass of KMnO₄} = 0.010625 \, \text{moles} \times 158.04 \, \text{g/mol} = 1.679 \, \text{g}
$$
Final Answer:
The mass of KMnO₄ in the solution is 1.68 grams (rounded to three significant figures).
Explanation:
In this problem, we first converted the given volume from milliliters to liters to match the unit used in the molarity formula. Then, using the molarity of the solution, we determined the number of moles of KMnO₄. Finally, we used the molar mass of KMnO₄ to convert moles into grams, giving us the required mass of the solute in the solution. This process involves applying basic concepts of molarity, stoichiometry, and the calculation of molar mass.