Sure! To find the mass of potassium dichromate (K₂Cr₂O₇) required to prepare 0.75 liters of a 0.01 M solution, we follow these steps:
1. Determine the molar mass of K₂Cr₂O₇:
The molar mass is calculated by summing the atomic masses of all the atoms in the compound:
- Potassium (K): 2 atoms with atomic mass of 39.1 g/mol each
- Chromium (Cr): 2 atoms with atomic mass of 52 g/mol each
- Oxygen (O): 7 atoms with atomic mass of 16 g/mol each
So, the molar mass of K₂Cr₂O₇ is:
[tex]\[
2 \times 39.1 \, \text{g/mol} + 2 \times 52 \, \text{g/mol} + 7 \times 16 \, \text{g/mol}
\][/tex]
[tex]\[
= 78.2 \, \text{g/mol} + 104 \, \text{g/mol} + 112 \, \text{g/mol}
\][/tex]
[tex]\[
= 294.2 \, \text{g/mol}
\][/tex]
2. Calculate the moles of K₂Cr₂O₇ required:
Moles ([tex]\(n\)[/tex]) can be calculated using the formula:
[tex]\[
n = C \times V
\][/tex]
where [tex]\(C\)[/tex] is the concentration (molarity) and [tex]\(V\)[/tex] is the volume of the solution in liters. Given that [tex]\(C = 0.01 \, \text{M}\)[/tex] and [tex]\(V = 0.75 \, \text{L}\)[/tex]:
[tex]\[
n = 0.01 \, \text{M} \times 0.75 \, \text{L}
\][/tex]
[tex]\[
= 0.0075 \, \text{moles}
\][/tex]
3. Calculate the mass of K₂Cr₂O₇ required:
The mass ([tex]\(m\)[/tex]) of K₂Cr₂O₇ required is found by multiplying the moles of K₂Cr₂O₇ by its molar mass:
[tex]\[
m = n \times \text{Molar mass}
\][/tex]
[tex]\[
= 0.0075 \, \text{moles} \times 294.2 \, \text{g/mol}
\][/tex]
[tex]\[
= 2.2065 \, \text{g}
\][/tex]
Therefore, the mass of potassium dichromate (K₂Cr₂O₇) that must be used to prepare 0.75 liters of a 0.01 M solution is approximately 2.2065 grams.
