A common way of producing hydrogen gas in the lab is by reacting zinc with hydrochloric acid.

Zn (s) + 2 HCl (aq) -> ZnCl2 (aq) + H2 (g)
A sample of impure zinc, of mass 5.10g, reacted with an excess of hydrochloric acid solution 3.0 mol dm-3 concentration. In the end 1.7dm-3 of hydrogen was obtained. Calculate the percentage impurities in the zinc sample.

What are the conditions? T, P? I will assume STP but technically this problem can't be worked without that informatiion.

1.7 dm-3 H2 produced. Convert to mols. That's 1.7 x (1 mol/22.4 dm-3) = ?
Convert to mols Zn. mols Zn = mols H2 (look at the coefficients in the balanced equation).
Then mols Zn x atomic mass Zn = grams Zn.
% Zn = (g Zn/5.10)*100 = ?
% impurities = 100-%Zn.

To calculate the percentage impurities in the zinc sample, you need to determine the amount of pure zinc used in the reaction. Here's how you can do that:

1. Calculate the number of moles of hydrogen gas produced:
Given volume of hydrogen gas = 1.7 dm³
Since the molar ratio between zinc and hydrogen gas is 1:1, the number of moles of hydrogen gas produced is also 1.7 mol.

2. Determine the limiting reactant:
To determine the limiting reactant, compare the number of moles of hydrogen gas produced with the number of moles of zinc that could have produced that amount of hydrogen gas.
The balanced equation indicates that 1 mole of zinc produces 1 mole of hydrogen gas. Therefore, the number of moles of zinc required is also 1.7 mol.

3. Calculate the molar mass of zinc:
The molar mass of zinc (Zn) is 65.38 g/mol.

4. Calculate the mass of pure zinc:
Mass of pure zinc = number of moles of zinc × molar mass of zinc
Mass of pure zinc = 1.7 mol × 65.38 g/mol = 111.166 g

5. Calculate the mass of impurities:
Mass of impurities = Mass of impure zinc - Mass of pure zinc
Mass of impurities = 5.10 g - 111.166 g = -106.066 g (Note: A negative mass indicates an error in calculation.)

6. Calculate the percentage impurities:
Percentage impurities = (Mass of impurities / Mass of impure zinc) × 100
Percentage impurities = (-106.066 g / 5.10 g) × 100 = -2081.25%

Based on the calculation, it seems there was an error either in the given mass of impure zinc or the calculation. Please recheck the values provided, and make sure they are accurate.