Calculating pH of the 1,96 % H3PO4 solution

[brunetteangel]

Homework Statement

Calculate pH of the 1,96% solution of H3PO4 (ρ≈1 g/cm^3). Take in account only the first constant of dissociation (7,5 * 10^-3 mol/cubic dm). The reduction of the concentration of H3PO4 because of dissociation can be ignored.

% = 1,96%
ρ (H3PO4) ≈1 g/cm^3
K = 7,5 * 10^-3 mol/cubic dm

Homework Equations

No equations in this task.

The Attempt at a Solution

Couldn't even attempt to solve it, because I don't know how to put the information together.

 

[Borek]

Convert to the molar concentration first.

You don't know anything about calculating pH of a weak acid? Equilibrium? Dissociation constants?

 

[brunetteangel]

I know a few formulas, but I think I can't use any of them in this task yet, because I don't have enough information.

And which formula is used for molar concentration, this one:

c (substance) = n (substance) / V (whole solution volume)

or this one:

b (substance) = n (substance) / m (mass of solvent)

I know that pH can be calculated as

pH = -log [H+] / mol dm^-3

but that doesn't help at the moment. :/

nor this one:

[H+] = Kw / [OH-]

I also know this:

K = alpha^2 * c

But none of this helps. :/

 

[Borek]

There is enough information.

First things first - you have to find a way to convert a %w/w concentration (given) to the molar concentration.

Then it will be about dissociation. Can you write reaction equation for the first step of the phosphoric acid dissociation? Can you write formula for the equilibrium constant for this reaction? This will be identical to the definition of the dissociation constant K_a1 (given in the question, just marked K).

 

[DeeNos]

I would approach this problem by first understanding the key variables and their relationships. The given concentration, percentage, and density of the H3PO4 solution indicate that the solution is 1,96% by mass and has a density of 1 g/cm^3. The dissociation constant, K, is also provided and is a measure of the strength of the acid.

To calculate the pH of the solution, we need to use the equation pH = -log[H+], where [H+] is the concentration of hydrogen ions in the solution. However, we are only given the dissociation constant, K, which is related to the concentration of H+ by the equation K = [H+]^3. Therefore, we can rearrange this equation to solve for [H+] and substitute it into the pH equation.

[H+] = (K)^(1/3) = (7,5 * 10^-3)^(1/3) = 0.02 mol/cubic dm

Now, we can plug this value into the pH equation:

pH = -log(0.02) = 1.7

Therefore, the pH of the 1,96% H3PO4 solution is 1.7. This indicates that the solution is acidic, as a pH below 7 is considered acidic.

It is also important to note that the reduction of the concentration of H3PO4 due to dissociation can be ignored in this calculation, as stated in the problem. This is because the concentration of H3PO4 is already very low (1,96% or 0.02 mol/cubic dm), so the impact of dissociation on the overall concentration is minimal.

In conclusion, by understanding the relationships between concentration, dissociation constant, and pH, we were able to calculate the pH of the given 1,96% H3PO4 solution.