To find the volume of the new solution when the concentration is changed, we need to follow these steps:
1. Determine the number of moles of solute present in the initial solution:
- The concentration (C) of the initial solution is 1.75 M (moles per liter).
- The volume (V) of the initial solution is 84.0 milliliters (which is 0.084 liters as 1 liter = 1000 milliliters).
The formula to calculate moles (n) is:
[tex]\[
n = C \times V
\][/tex]
Plugging in the initial values:
[tex]\[
n = 1.75 \, \text{M} \times 0.084 \, \text{L} = 0.147 \, \text{moles}
\][/tex]
So, the initial solution contains 0.147 moles of sodium bromide (NaBr).
2. Calculate the new volume of the solution which has the same moles but a different concentration:
- The final concentration (C') is 1.00 M.
- The number of moles of solute remains the same at 0.147 moles.
The formula to find the volume of a solution given its concentration and the number of moles is:
[tex]\[
V' = \frac{n}{C'}
\][/tex]
Plugging in the values:
[tex]\[
V' = \frac{0.147 \, \text{moles}}{1.00 \, \text{M}} = 0.147 \, \text{L}
\][/tex]
Converting this volume back to milliliters:
[tex]\[
0.147 \, \text{L} \times 1000 \, \text{mL/L} = 147.0 \, \text{mL}
\][/tex]
Thus, the volume of the new solution is 147.0 milliliters.
