# Find the concentration of protons

Lifeforbetter
Homework Statement:
NaOH 1M 100 mL + H2SO4 1M 100mL
Find the concentration of proton after mixed?
Relevant Equations:
H2SO4 + H2O -> H3O+ + HSO4-
After mixed, the volume is 200mL
I am confused. The mol of H2SO4 is M*V
1M*100mL or 1M*200mL ?
Finding the concentration of proton means the Molarity for H3O+ right? mol/volume
H2SO4 + H2O -> H3O+ + HSO4-
Mol H3O+ = Mol H2SO4?

Homework Helper
What effect does the reaction with NaOH have?

Lifeforbetter
What effect does the reaction with NaOH have?
2NaOH + H2SO4 -> Na2SO4 + 2H2O

Homework Helper
Do you have twice as much NaOH as H2SO4?

Lifeforbetter
Do you have twice as much NaOH as H2SO4?
Mol of NaOH is 0.1 mol

Homework Helper
You have 100 mL of 1M. how many moles is that?

Lifeforbetter
You have 100 mL of 1M. how many moles is that?
0.1 mol

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Lifeforbetter
Do you have twice as much NaOH as H2SO4?
Do you mean i need NaOH twice as much as H2SO4? So there's 0.5 mol excess of H2SO4? And produces H3O+ ?

Homework Helper
The reaction you wrote in #3 requires twice as much NaOH as H2SO4. What reaction occurs if you have the same amount of NaOH as H2SO4?

Lifeforbetter
The reaction you wrote in #3 requires twice as much NaOH as H2SO4. What reaction occurs if you have the same amount of NaOH as H2SO4?
Some H2SO4 will be left. All NaOH reacted?

Homework Helper
Which do you think is more likely - half the H2SO4 reacts completely, or all of it reacts half-way? Can you write an equation for the equimolar reaction of NaOH and H2SO4?

Lifeforbetter
Which do you think is more likely - half the H2SO4 reacts completely, or all of it reacts half-way? Can you write an equation for the equimolar reaction of NaOH and H2SO4?
2NaOH + H2SO4 -> Na2SO4 + 2H2O
0.1 mol---0.1mol-----0mol--------0mol
x mol-----0.5xmol----0.5xmol----0.5xmol
(0.1 - x)mol 0.1-(0.5x)mol

If it reacts halfway then
H2SO4 + NaOH -> NaHSO4 + H2O
H+ + H2O -> H3O+
Is it?

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Homework Helper
Yes, that is correct. HSO4- is a weak acid with a pKa of 1.99. Can you work out the proton concentration in the solution?

Lifeforbetter
Yes, that is correct. HSO4- is a weak acid with a pKa of 1.99. Can you work out the proton concentration in the solution?
Is it 0.5 mol?

Homework Helper
Gold Member
Have you figured yet that resulting "moles" of HSO4-1 becomes 'first' 0.1 moles, and that Ka=10^(-1.99) ? One mole of NaOH reacts with one mole H2SO4 to give one mole of the bisulfate ion. The Ka is weak but not too weak. You could try an equilibrium calculation if you want.

You may continue with formal concentration of 0.1moles bisulfate per 0.2 liters solution; what is that in formality?

If x is the molarity of hydronium ion then you can form (x^2)/(0.5-x)=10^-1.99 and solve the simple quadratic equation.

Lifeforbetter
Have you figured yet that resulting "moles" of HSO4-1 becomes 'first' 0.1 moles, and that Ka=10^(-1.99) ? One mole of NaOH reacts with one mole H2SO4 to give one mole of the bisulfate ion. The Ka is weak but not too weak. You could try an equilibrium calculation if you want.

You may continue with formal concentration of 0.1moles bisulfate per 0.2 liters solution; what is that in formality?

If x is the molarity of hydronium ion then you can form (x^2)/(0.5-x)=10^-1.99 and solve the simple quadratic equation.
I don't understand your first question..

concentration of HSO4 = 0.5 M ?
Do you mean that the concentration of HSO4 that left after reacted with NaOH?

Concentration of proton = concentration of H3O+?

If x is the molarity of hydronium ion then you can form (x^2)/(0.5-x)=10^-1.99 how to get to this equation?

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Homework Helper
Gold Member
I don't understand your first question..

concentration of HSO4 = 0.5 M ?
Do you mean that the concentration of HSO4 that left after reacted with NaOH?

Concentration of proton = concentration of H3O+?

If x is the molarity of hydronium ion then you can form (x^2)/(0.5-x)=10^-1.99 how to get to this equation?
My first question: Yes, but it does not stay that way. HSO4-1 is a weak acid (not too weak) and it dissociates. The formal concentration is 0.5 F but the MOLAR concentration becomes less because the acid dissociates.

Look again at that pKa.
The acid dissociation constant for bisulfate ion is 1.02x10-2.

Homework Helper
Gold Member
Let me write the quadratic equation a little better:
(x2)/(0.5-x)=1.02*10-2

The asterisk is the multiplication symbol to avoid confusing the "x" symbols.

Lifeforbetter
I don't understand.. so in order to count proton concentration. What its required?

Lifeforbetter
No. I have to understand the basic theory first. I will come back.

• symbolipoint
Homework Helper
Gold Member
No. I have to understand the basic theory first. I will come back.
Good Idea. If enrollment in a community college is your option, you could, if you have enough Mathematics qualification, study "Elementary Chemistry" to build some of the basics of Stoichiometry and understanding of some simpler inorganic reaction knowledge. Then again if you have the additional Math requirements, you can continue on to study General Chemistry; and in either first or second of the semesters of it, you will study equilibrium of weak acids and bases.

Lifeforbetter
Have you figured yet that resulting "moles" of HSO4-1 becomes 'first' 0.1 moles, and that Ka=10^(-1.99) ? One mole of NaOH reacts with one mole H2SO4 to give one mole of the bisulfate ion. The Ka is weak but not too weak. You could try an equilibrium calculation if you want.

You may continue with formal concentration of 0.1moles NaHSO4 per 0.2 liters solution; what is that in formality?

If x is the molarity of hydronium ion then you can form (x^2)/(0.5-x)=10^-1.99 and solve the simple quadratic equation.
Ok. So 0.1 mol of NaOH and 0.1 mol of H2SO4 reacted half way.. to give 0.1 mol of NaHSO4.
So what reaction happen next? Since there is no NaOH left. My goal is to find concentration of H+ in NaHSO4?

Homework Helper
Gold Member
Ok. So 0.1 mol of NaOH and 0.1 mol of H2SO4 reacted half way.. to give 0.1 mol of NaHSO4.
So what reaction happen next? Since there is no NaOH left. My goal is to find concentration of H+ in NaHSO4?

... If enrollment in a community college is your option, you could, if you have enough Mathematics qualification, study "Elementary Chemistry" to build some of the basics of Stoichiometry and understanding of some simpler inorganic reaction knowledge. Then again if you have the additional Math requirements, you can continue on to study General Chemistry; and in either first or second of the semesters of it, you will study equilibrium of weak acids and bases.

Lifeforbetter
Ok.
H2SO4 + NaOH -> NaHSO4 + H2O
H = 0.1 mol / 0.2 L = 0.5 M

Homework Helper
No. The formal concentration of HSO4- is 0.5M. You have to consider the dissociation
HSO4- + H2O → H3O+ + SO42-
You have been given the equilibrium constant for this reaction. Can you use it to calculate the concentration of H3O+?

Lifeforbetter
No. The formal concentration of HSO4- is 0.5M. You have to consider the dissociation
HSO4- + H2O → H3O+ + SO42-
You have been given the equilibrium constant for this reaction. Can you use it to calculate the concentration of H3O+?
The coefficient between HSO4- and H3O+ are the same? (The concentration not the same? That is 0.5 M?) What is F? Isn't mole/volume = M ?
Which equation to use equilibrium constant formula to find concentration of H3O+ from this equation? HSO4- + H2O → H3O+ + SO42- ?
What is concentration of H2O?

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Lifeforbetter
Let me write the quadratic equation a little better:
(x2)/(0.5-x)=1.02*10-2
I don't know where this come from.. 0.5 - x and x refers to what concentration..
But i calculate
x = 0.01 +- 0.05##\sqrt2##

Homework Helper
x is the concentration of H3O+, which is equal to the concentration of SO42-. 0.5-x is the concentration of HSO4-. We ignore the concentration of water as it is effectively constant.

Lifeforbetter
x is the concentration of H3O+, which is equal to the concentration of SO42-. 0.5-x is the concentration of HSO4-. We ignore the concentration of water as it is effectively constant.
x = 0.0665 M ?

Homework Helper
Gold Member
No. The formal concentration of HSO4- is 0.5M. You have to consider the dissociation
HSO4- + H2O → H3O+ + SO42-
You have been given the equilibrium constant for this reaction. Can you use it to calculate the concentration of H3O+?
Just in being fair, he may need to reread or recheck the distinction between FORMALITY and MOLARITY.

Homework Helper
Gold Member
x is the concentration of H3O+, which is equal to the concentration of SO42-. 0.5-x is the concentration of HSO4-. We ignore the concentration of water as it is effectively constant.