What is the mass of potassium iodide (KI molar mass 166 g/mol) in 50.0 mL of 0.575 M KI? Report your answer to three digits, for example, 0.567, 1.54, and do not include the unit.
The Correct Answer and Explanation is:
Correct Answer:
4.77
Explanation
To find the mass of potassium iodide (KI) in a solution, we follow a step-by-step process using the molarity formula and molar mass.
Step 1: Understand What’s Given
- Volume of the solution: 50.0 mL
- Molarity (concentration): 0.575 M (mol/L)
- Molar mass of KI: 166 g/mol
We want to find the mass (in grams) of KI in this volume of solution.
Step 2: Convert Volume to Liters
Molarity is defined in moles per liter, so we need to convert milliliters to liters: 50.0 mL=0.0500 L50.0\ \text{mL} = 0.0500\ \text{L}50.0 mL=0.0500 L
Step 3: Use the Molarity Formula
Molarity (M) is defined as: M=moles of soluteliters of solutionM = \frac{\text{moles of solute}}{\text{liters of solution}}M=liters of solutionmoles of solute
Rearranged to find moles: moles of KI=M×volume in L=0.575 mol/L×0.0500 L=0.02875 mol\text{moles of KI} = M \times \text{volume in L} = 0.575\ \text{mol/L} \times 0.0500\ \text{L} = 0.02875\ \text{mol}moles of KI=M×volume in L=0.575 mol/L×0.0500 L=0.02875 mol
Step 4: Convert Moles to Grams
Now, use the molar mass of KI (166 g/mol) to find the mass: mass=moles×molar mass=0.02875 mol×166 g/mol=4.7725 g\text{mass} = \text{moles} \times \text{molar mass} = 0.02875\ \text{mol} \times 166\ \text{g/mol} = 4.7725\ \text{g}mass=moles×molar mass=0.02875 mol×166 g/mol=4.7725 g
Step 5: Round to 3 Significant Digits
Since the given values (50.0 mL and 0.575 M) have 3 significant digits, we must round the final answer accordingly: 4.77\boxed{4.77}4.77
This is the mass of KI in 50.0 mL of a 0.575 M solution.
