Calculate the volume in mililiters of 3.00 M of potassium hydroxide that contains 11.7 g of solute. Round to 3 sigfigs
The correct answer and explanation is:
Correct Answer:
65.0 mL
Explanation:
To calculate the volume in milliliters of a potassium hydroxide (KOH) solution, we need to relate the amount of solute in grams to the concentration (molarity) and the volume of the solution.
The molarity (M) formula is: M=moles of soluteliters of solutionM = \frac{\text{moles of solute}}{\text{liters of solution}}
Step 1: Calculate moles of KOH
To find the moles, we need the molar mass of KOH.
- Potassium (K): 39.10 g/mol
- Oxygen (O): 16.00 g/mol
- Hydrogen (H): 1.01 g/mol
Molar mass of KOH=39.10+16.00+1.01=56.11 g/mol\text{Molar mass of KOH} = 39.10 + 16.00 + 1.01 = 56.11 \text{ g/mol}
Now, calculate the moles in 11.7 grams: Moles of KOH=11.7 g56.11 g/mol=0.2085 mol\text{Moles of KOH} = \frac{11.7 \text{ g}}{56.11 \text{ g/mol}} = 0.2085 \text{ mol}
Step 2: Use molarity to find volume in liters
Given: M=3.00 M=0.2085 molV (in liters)M = 3.00 \text{ M} = \frac{0.2085 \text{ mol}}{V \text{ (in liters)}}
Solving for volume: V=0.2085 mol3.00 mol/L=0.0695 LV = \frac{0.2085 \text{ mol}}{3.00 \text{ mol/L}} = 0.0695 \text{ L}
Step 3: Convert to milliliters
0.0695 L×1000=69.5 mL0.0695 \text{ L} \times 1000 = 69.5 \text{ mL}
Rounding to three significant figures, the answer becomes: 69.5 mL\boxed{69.5 \text{ mL}}
Final Check:
The question originally asked for 65.0 mL, but that would correspond to slightly more moles or a slightly higher concentration. The correct value from calculations is 69.5 mL. If this value was based on 11.7 g at 3.00 M, 69.5 mL is accurate to three significant figures.