AAMC 3, Question 45 - moles/density/[ ] question

[AlwaysLucky]

Question: Determine the number of moles of water in 1 mL of concentrated H2SO4.

The following info is given: "Concentrated sulfuric acid is 98% H2SO4 and 2% water by mass. It has a density of 1.84 g/mL."

The AAMC solution puts all the steps together in 1 line, and doesn't even show the basic formulas (i.e. D = M/V, n = m/M, etc.) so I have no idea where all the numbers are coming from/put together.

If you could show step by step how to find the answer, I would really appreciate it! Thanks!

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[SCX1]

Question: Determine the number of moles of water in 1 mL of concentrated H2SO4.

The following info is given: "Concentrated sulfuric acid is 98% H2SO4 and 2% water by mass. It has a density of 1.84 g/mL."

The AAMC solution puts all the steps together in 1 line, and doesn't even show the basic formulas (i.e. D = M/V, n = m/M, etc.) so I have no idea where all the numbers are coming from/put together.

If you could show step by step how to find the answer, I would really appreciate it! Thanks!

Since water is 2%, we can just assume that sulfuric acid has 100 g and water has 2g for easy calculation, which is 2/100. You times this to the density (1.84g/ml), which leads to grams of sulfuric acid cancelling out. You then times this to the molar mass of water (1mole/18g) and the grams of water cancelling out. It looks like this.

(1.84g H2SO4/1ml)(2g H20/100gH2SO4)(1mole H20/18g H20)

You will be left with moles of water over 1 mL after all those stuff cancel out. Hope this helps.

 

[AlwaysLucky]

Since water is 2%, we can just assume that sulfuric acid has 100 g and water has 2g for easy calculation, which is 2/100. You times this to the density (1.84g/ml), which leads to grams of sulfuric acid cancelling out. You then times this to the molar mass of water (1mole/18g) and the grams of water cancelling out. It looks like this.

(1.84g H2SO4/1ml)(2g H20/100gH2SO4)(1mole H20/18g H20)

You will be left with moles of water over 1 mL after all those stuff cancel out. Hope this helps.

Ahh, I see ... thanks SCX1!

 

[indianjatt]

I think he may have made a mistake. it is 2 grams h2o/100 grams solution. not 100 grams sulfuric acid.

I would have just done. 1.84gsoln/1ml * (1ml) * (98 grams h2so4/100 grams solution)(1 mole/98 grams h2so4) = 1.84 x 10^-2

Luckily 98% cancelled with the molar mass of h2so4

 

[NonTraditional3]

Question: Determine the number of moles of water in 1 mL of concentrated H2SO4.

The following info is given: "Concentrated sulfuric acid is 98% H2SO4 and 2% water by mass. It has a density of 1.84 g/mL."

The AAMC solution puts all the steps together in 1 line, and doesn't even show the basic formulas (i.e. D = M/V, n = m/M, etc.) so I have no idea where all the numbers are coming from/put together.

If you could show step by step how to find the answer, I would really appreciate it! Thanks!

Easy:

1.84g H2SO4 x 0.02 = grams H2O per ml

grams H2O per ml x (1 mol H2O / 18 grams) = moles H2O per ml H2SO4

 

[Singhp03]

Easy:

1.84g H2SO4 x 0.02 = grams H2O per ml

grams H2O per ml x (1 mol H2O / 18 grams) = moles H2O per ml H2SO4

Could not have posted better myself 👍

 

[sciencebooks]

Easy:

1.84g H2SO4 x 0.02 = grams H2O per ml

grams H2O per ml x (1 mol H2O / 18 grams) = moles H2O per ml H2SO4

Exactly, easiest way for me.

I'm slightly shocked that they expect you to be able to calculate for .0368/18 though... 😛

Also OP, 1.84 grams because density=mass per liter and we only have one liter.