To determine the number of moles in a 4.5-liter HCl solution with a molarity of 6.0 moles per liter, follow these steps:
1. Identify the known values:
- Volume of the solution (V) = 4.5 liters.
- Molarity of the solution (M) = 6.0 moles per liter.
2. Understand the relationship between volume, molarity, and moles:
- The molarity (M) of a solution is defined as the number of moles of a solute (n) divided by the volume of the solution in liters (V).
- Mathematically, this relationship is expressed as:
[tex]\[
\text{Molarity (M)} = \frac{\text{Number of moles (n)}}{\text{Volume in liters (V)}}
\][/tex]
3. Rearrange the formula to find the number of moles (n):
- Multiply both sides of the equation by the volume (V) to isolate the number of moles (n):
[tex]\[
\text{Number of moles (n)} = \text{Molarity (M)} \times \text{Volume (V)}
\][/tex]
4. Substitute the known values into the equation:
- Molarity (M) = 6.0 moles per liter.
- Volume (V) = 4.5 liters.
[tex]\[
\text{Number of moles (n)} = 6.0 \text{ moles/L} \times 4.5 \text{ L}
\][/tex]
5. Calculate the number of moles:
- Perform the multiplication:
[tex]\[
\text{Number of moles (n)} = 6.0 \times 4.5 = 27.0 \text{ moles}
\][/tex]
Therefore, the number of moles in a 4.5-liter HCl solution with a molarity of 6.0 is [tex]\( 27.0 \)[/tex] moles.
