To find the volume of a 4.0 M LiBr solution that can be made using 100.0 grams of LiBr, follow these steps:
### Step 1: Calculate the number of moles of LiBr
First, we need to determine how many moles of LiBr are present in 100.0 grams.
Given:
- Mass of LiBr ([tex]\(m_{\text{LiBr}}\)[/tex]) = 100.0 grams
- Molar mass of LiBr ([tex]\(M_{\text{LiBr}}\)[/tex]) = 86.44 g/mol
The number of moles ([tex]\(n\)[/tex]) is calculated by:
[tex]\[
n = \frac{m_{\text{LiBr}}}{M_{\text{LiBr}}}
\][/tex]
Plug in the numbers:
[tex]\[
n = \frac{100.0\ \text{g}}{86.44\ \text{g/mol}} \approx 1.1569\ \text{mol}
\][/tex]
### Step 2: Calculate the volume of LiBr solution
Now, using the molarity formula, which is the number of moles of solute per liter of solution, we can find the volume of the solution.
Given:
- Moles of LiBr ([tex]\(n\)[/tex]) ≈ 1.1569 mol
- Concentration ([tex]\(C\)[/tex]) = 4.0 M (mol/L)
The formula for volume [tex]\(V\)[/tex] in liters is:
[tex]\[
V = \frac{n}{C}
\][/tex]
Plug in the numbers:
[tex]\[
V = \frac{1.1569\ \text{mol}}{4.0\ \text{mol/L}} \approx 0.2892\ \text{L}
\][/tex]
### Conclusion
The volume of a 4.0 M LiBr solution that can be made using 100.0 grams of LiBr is approximately 0.2892 liters.
