Let's solve this problem step-by-step:
1. Identify the given values:
- Volume of the solution ([tex]\( V \)[/tex]) = 0.400 liters (L)
- Molarity of the solution ([tex]\( M \)[/tex]) = 0.350 moles per liter (M)
2. Determine the molar mass of KBr:
KBr is composed of potassium (K) and bromine (Br).
- Atomic mass of potassium (K) = 39.1 g/mol
- Atomic mass of bromine (Br) = 79.9 g/mol
Therefore, the molar mass of KBr ([tex]\( M_{\text{KBr}} \)[/tex]) is:
[tex]\[
M_{\text{KBr}} = 39.1 \, \text{g/mol} + 79.9 \, \text{g/mol} = 119.0 \, \text{g/mol}
\][/tex]
3. Calculate the number of moles of KBr in the solution:
Molarity is defined as the number of moles of solute per liter of solution ([tex]\( M = \frac{\text{moles}}{\text{liters}} \)[/tex]).
Rearranging this formula to find the number of moles ([tex]\( n \)[/tex]):
[tex]\[
n = M \times V
\][/tex]
Substituting the given values:
[tex]\[
n = 0.350 \, \text{M} \times 0.400 \, \text{L} = 0.140 \, \text{moles}
\][/tex]
4. Calculate the mass of KBr in the solution:
The mass of KBr can be determined using the formula:
[tex]\[
\text{mass} = n \times M_{\text{KBr}}
\][/tex]
Substituting the values of [tex]\( n \)[/tex] and [tex]\( M_{\text{KBr}} \)[/tex]:
[tex]\[
\text{mass} = 0.140 \, \text{moles} \times 119.0 \, \text{g/mol} = 16.66 \, \text{grams}
\][/tex]
Therefore, the mass of KBr in 0.400 liters of a 0.350 M solution is 16.66 grams.
