The density of a solution of hydrochloric acid is 1.0929 g/cc, and it is 19.00 percent by mass. What
volume of the solution (in milliliters) do you need to supply 30.0 g of hydrochloric acid?
I'm not sure how to start
1.0929 g/mL x ?mL x 0.19 = 30.0
Solve for ?mL.
To find the volume of the solution needed to supply a certain mass of hydrochloric acid, we can follow these steps:
Step 1: Convert the mass of hydrochloric acid to a percentage by dividing it by the total mass of the solution.
In this case, the mass of hydrochloric acid is 30.0 g and the solution is 19.00% by mass. We need to convert the mass of hydrochloric acid to a percentage:
Percentage of hydrochloric acid = (mass of hydrochloric acid / total mass of the solution) * 100
Percentage of hydrochloric acid = (30.0 g / total mass of the solution) * 100
Step 2: Set up a proportion using the densities of the solution and hydrochloric acid.
The density of the solution is given as 1.0929 g/cc.
Density = mass / volume
The proportion can be set up as:
Density of solution / Density of hydrochloric acid = Volume of solution / Volume of hydrochloric acid
Step 3: Solve the proportion to find the volume of the solution.
Let's denote the volume of the solution as V_solution and the volume of hydrochloric acid as V_hydrochloric acid.
Density of hydrochloric acid = mass of hydrochloric acid / volume of hydrochloric acid
We are given the mass of hydrochloric acid as 30.0 g. Substituting the values, the proportion becomes:
1.0929 g/cc / (30.0 g / V_hydrochloric acid) = 1.0000 g/cc / (30.0 g / 30.0 mL)
Solving for V_hydrochloric acid:
V_hydrochloric acid = (1.0929 g/cc * 30.0 mL * 30.0 g) / (1.0000 g/cc * 30.0 g)
Simplifying:
V_hydrochloric acid = (98,670 g* mL) / (1,000 g)
V_hydrochloric acid = 98.67 mL
Step 4: Calculate the volume of the solution using the mass percentage and the volume of hydrochloric acid.
We have the mass percentage as 19.00%, so the mass of the solution can be calculated as:
Mass of solution = mass of hydrochloric acid / (percentage of hydrochloric acid / 100)
Mass of solution = 30.0 g / (19.00 / 100)
Mass of solution = 30.0 g / 0.1900
Mass of solution = 157.89 g
Finally, we can calculate the volume of the solution by dividing the mass of the solution by its density:
Volume of solution = mass of solution / density of solution
Volume of solution = 157.89 g / 1.0929 g/cc
Volume of solution = 144.42 cc
Step 5: Convert the volume of the solution from cc to milliliters.
1 cc is equal to 1 milliliter (ml).
Volume of solution in milliliters = 144.42 cc = 144.42 ml
Therefore, to supply 30.0 g of hydrochloric acid, you would need to provide 144.42 milliliters of the solution.