How many grams of NaCl are in a 12.45 mL sample of 0.50 M NaCl solution? The molar mass of sodium chloride is 58.44 g/mole.
The correct answer and explanation is:
First, the correct answer is 0.36 grams of NaCl.
To solve this, begin by understanding that molarity (M) represents moles of solute per liter of solution. A 0.50 M NaCl solution means there are 0.50 moles of NaCl dissolved in every 1 liter (1000 milliliters) of solution. To find the moles of NaCl in a smaller volume like 12.45 milliliters, a proportion is set up using the molarity formula: Moles of NaCl=Molarity×Volume (L)\text{Moles of NaCl} = Molarity \times \text{Volume (L)}
First, convert 12.45 mL to liters: 12.45 mL×1 L1000 mL=0.01245 L12.45\; \text{mL} \times \frac{1\; \text{L}}{1000\; \text{mL}} = 0.01245\; \text{L}
Next, multiply the molarity by the volume in liters: Moles of NaCl=0.50 M×0.01245 L=0.006225 moles NaCl\text{Moles of NaCl} = 0.50\; M \times 0.01245\; L = 0.006225\; \text{moles NaCl}
The next step converts moles of NaCl to grams using the molar mass: Mass (g)=Moles×Molar Mass (g/mol)\text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)}
So, Mass of NaCl=0.006225 mol×58.44 g/mol=0.3638 g\text{Mass of NaCl} = 0.006225\; \text{mol} \times 58.44\; \text{g/mol} = 0.3638\; \text{g}
Rounded to two significant figures to match the input values, the final answer is 0.36 grams of NaCl.
This problem illustrates how molarity connects volume, moles, and mass. Such calculations are vital in preparing solutions in chemistry labs. Knowing how much solute is present allows chemists to precisely control reactions and ensure accurate experimental results. Miscalculations can lead to incorrect concentrations, affecting the reliability and safety of experiments. Understanding units is equally important. Always convert milliliters to liters when using molarity equations since molarity is defined per liter. Finally, when multiplying by the molar mass, the units cancel properly, leaving grams as the final unit. This reinforces the importance of dimensional analysis to catch potential mistakes.