what volume of a concentrated HCl solution which is 36% HCl by mass and has a density of 1.179g/ml should be used to make 5.30L of an HCl solution with a pH of 1.8?
To find the volume of a concentrated HCl solution needed to make a specific volume and pH of a solution, we need to consider a few factors: the concentration of the concentrated HCl solution, its density, and the desired pH of the final solution.
Step 1: Determine the number of moles of HCl needed for the desired pH.
The pH of the solution indicates its acidity, with a lower pH value indicating higher acidity. pH 1.8 is relatively acidic, so we need to calculate the number of moles of HCl required to achieve this acidity. Since the pH of a strong acid solution such as HCl is equal to the negative logarithm of its hydrogen ion concentration, we can determine the hydrogen ion concentration using the formula:
[H+] = 10^(-pH)
[H+] = 10^(-1.8)
[H+] = 0.0158 M (moles per liter)
Step 2: Calculate the volume of the concentrated HCl solution required.
To determine the volume of the concentrated HCl solution needed, we can utilize the equation:
moles = concentration x volume
However, since we are given the density instead of concentration, we need to convert the information. The density of the concentrated HCl solution is given as 1.179 g/ml, and we know that the solution is 36% HCl by mass.
First, we need to calculate the concentration of the HCl solution.
concentration = (mass of HCl / mass of solution) x 100
mass of HCl = 36% of the mass of the solution
mass of HCl = 0.36 x mass of the solution
Since we don't know the mass of the solution yet, we can assign a variable, let's say "x". Then, the mass of HCl is 0.36x.
The mass of the HCl solution is equal to its volume (V) multiplied by its density (D).
mass of the solution = V x D
Substituting the values, we get:
mass of the HCl solution = V x 1.179 g/ml
Now we can replace the mass of the solution with V x 1.179 g/ml in the concentration equation:
0.36x = (0.36x / (V x 1.179)) x 100
0.0036x = (0.36x / (V x 1.179))
Now we can simplify the equation:
0.0036 = 0.36 / (V x 1.179)
To isolate V, we can rearrange the equation:
V = 0.36 / (1.179 x 0.0036)
V ≈ 117.9 ml
Step 3: Convert the volume to liters.
To convert the volume from milliliters to liters, divide the volume by 1000:
V = 117.9 ml / 1000 ml/L
V ≈ 0.1179 L
Therefore, approximately 0.1179 liters (or 117.9 ml) of the concentrated HCl solution should be used to make 5.30 liters of an HCl solution with a pH of 1.8.