Final answer:
To find the required mass of KBr solute for a 0.178 M solution in 470.3 ml, convert the volume to liters, use the given molarity to calculate moles, and multiply by the molar mass of KBr to get the mass. The calculated mass is approximately 9.97 g, suggesting a typo in the provided options with the closest being 9.22 g.
Step-by-step explanation:
To calculate the mass of solute required to produce 470.3 ml of a 0.178 M KBr solution, you can follow these steps:
- Use the molarity equation: M = moles of solute / liters of solution to find the number of moles of KBr needed for the solution.
- Convert the volume from milliliters to liters by dividing by 1000.
- Calculate the moles of KBr required using the given molarity and the volume in liters.
- Determine the molar mass of KBr (K = 39.10 g/mol, Br = 79.90 g/mol, total = 119.00 g/mol).
- Multiply the moles of KBr by the molar mass to find the mass of KBr in grams.
Putting these steps into practice:
- 0.4703 L (since 470.3 ml is equal to 0.4703 L)
- Calculate the moles: 0.178 mol/L * 0.4703 L = 0.0837634 mol
- Calculate the mass: 0.0837634 mol * 119.00 g/mol = 9.97 g
As the result is not one of the given choices, we can assume there might have been a typo in the options provided. The closest option to the accurate calculation is 9.22 g which seems to be a rounded-down figure. Therefore, the correct mass of KBr needed is approximately 9.97 g (or close to option B if we consider potential rounding).