sulfuric acid is a strong acid and dissociates in water as shown in reaction

H2SO4(aq)=2H^+(aq)+SO4^2-(aq)
what is the hydrogen ion concentration, in mol dm^-3,when 1.50g of sulfuric acid is dissolved in water to give 0.500dm^3 of solution ?show all of your working and give your answer to three significant figures.

Hello zak. What level is this course? If you want an approximate answer, and from the ionization equation in the problem I think that is what you want, it is as follows:

mols H2SO4 = 1.50g/molar mass H2SO4 = about 0.015 but you need to be more accurate.
mols H^+ = twice that (from two hydrogen ions/molecule)= ?.
Then (H) in M = mols/L = ?/0.500 = xx?.

In reality it is less than that because H2SO4 is not a strong acid EXCEPT for the first ionization; i.e., the second ionization has a k2 = about 0.012. If you take that into account (H^+) = about 0.04M instead of about 0.06M.

To find the hydrogen ion concentration in mol dm^-3, we need to use the molar mass of sulfuric acid and the volume of the solution.

1. Calculate the number of moles of sulfuric acid:
First, we find the molar mass of sulfuric acid (H2SO4):
H: 1.01 g/mol x 2 = 2.02 g/mol
S: 32.07 g/mol
O: 16.00 g/mol x 4 = 64.00 g/mol
Total molar mass of H2SO4: 98.09 g/mol

Now, we can calculate the number of moles:
Number of moles = mass / molar mass
Number of moles = 1.50 g / 98.09 g/mol

2. Calculate the concentration:
Concentration (in mol dm^-3) = number of moles / volume (in dm^3)
Concentration = (1.50 g / 98.09 g/mol) / 0.500 dm^3

Now, we can solve this equation to get the hydrogen ion concentration in mol dm^-3.
Since we need the answer to three significant figures, let's round it to three decimal places.

Calculating this equation will give us the hydrogen ion concentration.