Question

How many moles of solute are in a 1.50 M solution of HCl with a volume of 7.98 liters?

Answer 1

Answer:

$\boxed {\boxed {\sf x\approx 12.0 \ moles \ HCl}}$

Explanation:

Molarity is a measure of concentration in moles per liter.

$molarity= \frac{moles \ of \ solute}{liters \ of solution}$

We know the solution has a volume of 7.98 liters and it has a molarity of 1.50 M HCl.

• 1 molar (M) is 1 mole per liter, so the molarity is also 1.50 moles of HCl per liter.

We know 2 values for the variables, but the value for moles of solute is unknown, so we use x.

• molarity= 1.50 mol HCl/L

• moles of solute=x

• liters of solution = 7.98 L

Substitute the values into the formula.

$1.50 \ mol \ HCl/L=\frac{x}{7.98 \ L}$

We are trying to solve for x, the moles of solute, so we must isolate the variable. It is being divided by 7.98 liters and the inverse of division is multiplication. Multiply both sides of the equation by 7.98 liters.

$7.98 \ L *1.50 \ mol \ HCl/L=\frac{x}{7.98 \ L} * 7.98 \ L$

$7.98 \ L *1.50 \ mol \ HCl/L=x$

The units of liters (L) cancel each other out.

$7.98 *1.50 \ mol \ HCl=x$

$11.97 \ mol \ HCl=x$

The original measurements of molarity and volume both have 3 significant figures, so our answer must have the same. For the number we found, that is the tenths place.

The 9 in the hundredth place tells us to round the 1 to a 2. We leave a 0 in the tenths place to ensure there are 3 significant figures.

$12.0 \ mol \ HCl \approx x$

There are approximately 12.0 moles of solute in the solution.