a) How much of the primary standard benzoic acid (FM 122.12, density 5 1.27 g/mL) should you weigh out to obtain a 100.0 mM aqueous solution in a volume of 250 mL?
The correct answer and explanation is :
To calculate how much benzoic acid you need to weigh out to obtain a 100.0 mM aqueous solution in a volume of 250 mL, we need to follow these steps:
Step 1: Understand the Problem
- The desired concentration of the solution is 100.0 mM (millimolar), which is 0.1000 moles per liter (since 1 mM = 0.001 mol/L).
- The volume of the solution is 250 mL (0.250 L).
- Benzoic acid has a molecular formula of C₆H₅COOH, with a molecular mass of 122.12 g/mol.
- The density of benzoic acid is 1.27 g/mL.
Step 2: Calculate the Moles Required
To find out how many moles of benzoic acid we need for a 100.0 mM solution in 250 mL, we use the formula for molarity:
[
\text{Moles of solute} = \text{Molarity} \times \text{Volume}
]
Substituting the values:
[
\text{Moles of benzoic acid} = 0.1000 \, \text{mol/L} \times 0.250 \, \text{L} = 0.0250 \, \text{mol}
]
So, we need 0.0250 moles of benzoic acid.
Step 3: Convert Moles to Mass
Now, we need to convert moles of benzoic acid to grams using the molecular weight of benzoic acid, which is 122.12 g/mol:
[
\text{Mass of benzoic acid} = \text{Moles} \times \text{Molar Mass}
]
[
\text{Mass of benzoic acid} = 0.0250 \, \text{mol} \times 122.12 \, \text{g/mol} = 3.053 \, \text{g}
]
So, you need to weigh out 3.053 g of benzoic acid.
Step 4: Verification Using Density
We can also verify this by using the density of benzoic acid (1.27 g/mL). To calculate how much volume corresponds to the mass of benzoic acid, we can use the formula:
[
\text{Volume of benzoic acid} = \frac{\text{Mass}}{\text{Density}}
]
[
\text{Volume of benzoic acid} = \frac{3.053 \, \text{g}}{1.27 \, \text{g/mL}} = 2.4 \, \text{mL}
]
Thus, 3.053 g of benzoic acid corresponds to 2.4 mL of liquid benzoic acid.
Final Answer:
We need to weigh out 3.053 g of benzoic acid to prepare 250 mL of a 100.0 mM aqueous solution.