A mixture of 10.00 mL of H2SO4 and 30.00 mL of HCl required 20.00 mL of 2.500 M NaOH

for complete reaction. When 30.00 mL of H2SO4 and 10.00 mL of HCl were used,
28.00 mL of 2.500 M NaOH were required. What were the concentrations of the acids?
[Both were 1.000 M]
H2SO4(aq) + 2NaOH(aq) Na2SO4(aq) + 2H2O(l)
HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l)

Let x = M H2SO4

and y = M NaOH
(Note that it takes 2 mols NaOH to react with 1 mol H2SO4.)
In words;
eqn 1: mols H2SO4 + mols HCl = mols NaOH
eqn 2: mols H2SO4 + mols HCl = mols NaOH
Change word equation to numbers.
10x*2 + 30y = 2.5*20 is eqn 1.
30x*2 + 10y = 2.5*28 is eqn 2.

Solve the two equations simultaneously for x and y.

To find the concentrations of the acids, we can use the concept of stoichiometry and the given information about the volumes and concentrations of the solutions. Let's break down the steps to solve the problem:

1. Calculate the amount of NaOH used in both reactions:
In the first reaction, 20.00 mL of 2.500 M NaOH were used. Since concentration (Molarity) is given as moles per liter, we can convert the volume to liters:
20.00 mL = 20.00 mL * (1 L / 1000 mL) = 0.020 L
Then, we can calculate the amount of NaOH used:
Amount of NaOH = 0.020 L * 2.500 mol/L = 0.050 mol

Similarly, in the second reaction, 28.00 mL of 2.500 M NaOH were used:
28.00 mL = 28.00 mL * (1 L / 1000 mL) = 0.028 L
Amount of NaOH = 0.028 L * 2.500 mol/L = 0.070 mol

2. Use the balanced chemical equations to determine the stoichiometric ratio between NaOH and the acids:
From the balanced chemical equations given, we know that 1 mole of H2SO4 reacts with 2 moles of NaOH, and 1 mole of HCl reacts with 1 mole of NaOH.

3. Calculate the amount of acids used in both reactions:
For the H2SO4 reaction:
Amount of H2SO4 = 0.050 mol * (1 mol H2SO4 / 2 mol NaOH) = 0.025 mol

For the HCl reaction:
Amount of HCl = 0.070 mol * (1 mol HCl / 1 mol NaOH) = 0.070 mol

4. Calculate the concentrations of the acids:
Concentration (Molarity) is defined as moles per liter.
For the H2SO4 reaction:
Volume of H2SO4 = 30.00 mL + 10.00 mL = 40.00 mL = 40.00 mL * (1 L / 1000 mL) = 0.040 L
Concentration of H2SO4 = 0.025 mol / 0.040 L = 0.625 M

For the HCl reaction:
Volume of HCl = 10.00 mL + 30.00 mL = 40.00 mL = 40.00 mL * (1 L / 1000 mL) = 0.040 L
Concentration of HCl = 0.070 mol / 0.040 L = 1.750 M

Therefore, the concentrations of the acids are:
H2SO4: 0.625 M
HCl: 1.750 M