What mass of sodium hydroxide (NaOH, molar mass = 40.0 g·mol–1) is needed to make 100.0 mL of a 0.125 M NaOH solution?
The Correct Answer and Explanation is:
Answer:
The mass of sodium hydroxide (NaOH) needed is:mass=molarity×volume (L)×molar mass\text{mass} = \text{molarity} \times \text{volume (L)} \times \text{molar mass}mass=molarity×volume (L)×molar massmass=0.125 mol/L×0.1000 L×40.0 g/mol=0.500 g\text{mass} = 0.125 \, \text{mol/L} \times 0.1000 \, \text{L} \times 40.0 \, \text{g/mol} = \boxed{0.500 \, \text{g}}mass=0.125mol/L×0.1000L×40.0g/mol=0.500g
Explanation
To prepare a solution with a specific concentration, it’s important to understand the relationship between molarity, volume, and mass. Molarity (M) is defined as the number of moles of solute per liter of solution. In this problem, we’re given the molarity (0.125 M) and the volume (100.0 mL) of the solution we want to prepare, and we’re asked to find the mass of sodium hydroxide (NaOH) required.
First, convert the volume from milliliters to liters since molarity is based on liters:100.0 mL=0.1000 L100.0 \, \text{mL} = 0.1000 \, \text{L}100.0mL=0.1000L
Next, calculate the number of moles of NaOH needed using the definition of molarity:moles of NaOH=0.125 mol/L×0.1000 L=0.0125 mol\text{moles of NaOH} = 0.125 \, \text{mol/L} \times 0.1000 \, \text{L} = 0.0125 \, \text{mol}moles of NaOH=0.125mol/L×0.1000L=0.0125mol
Then, use the molar mass of NaOH to convert moles to grams. The molar mass is given as 40.0 g/mol, which means 1 mole of NaOH weighs 40.0 grams:mass=0.0125 mol×40.0 g/mol=0.500 g\text{mass} = 0.0125 \, \text{mol} \times 40.0 \, \text{g/mol} = 0.500 \, \text{g}mass=0.0125mol×40.0g/mol=0.500g
Therefore, to prepare 100.0 mL of a 0.125 M NaOH solution, you need 0.500 grams of sodium hydroxide.
This calculation is essential in laboratory settings to ensure accurate solution concentrations, especially in titrations, pH adjustments, and chemical reactions. Incorrect measurements can lead to errors in experimental outcomes, so understanding how to calculate and prepare molar solutions is a fundamental skill in chemistry.
