A sample of impure magnesium was allowed to react with excess HCL solution. After 5.5 gram of the impure metal was treated with 0.3L of 0.6 M HCL, 0.0125 mole of HCL remained. Assuming the impurities do not react with the acid, what is the mass % of magnesium in the sample?
The Mg metal (the real stuff) reacts with the HCl as follows:
2HCl + Mg ==> MgCl2 + H2
moles HCl initially = M x L = 0.6 M x 0.3 L = 0.18 mols.
moles HCl remaining after reaction = 0.0125
moles HCl used in the reaction = 0.18 - 0.0125 = 0.1675
Convert 0.1675 mols HCl used to Mg used as follows:
0.1675 mols HCl x (1 mol Mg/2 mol HCl) = 0.08375 mols Mg used.
Convert that to grams. g = mols x atomic mass Mg = 2.03 g Mg
% Mg in the original sample = (mass Mg/mass sample)*100 = (2.03/5.5)* 100 = ? about 37%. Note: I have used more significant figures than allowed because the problem makes no effort to distinguish between 0.6 M and 0.3 L vs. 0.600 M and 0.300 L.
To determine the mass % of magnesium in the sample, we need to calculate the amount of magnesium that reacted with the HCl and compare it to the initial amount of impure magnesium.
First, let's calculate the amount of HCl that reacted with magnesium:
Amount of HCl initially = Volume of HCl x Concentration of HCl
= 0.3 L x 0.6 M
= 0.18 moles
Amount of HCl that remained = 0.0125 moles
Amount of HCl that reacted with magnesium = Amount of HCl initially - Amount of HCl that remained
= 0.18 moles - 0.0125 moles
= 0.1675 moles
Since the reaction between magnesium and HCl occurs in a 1:2 molar ratio, the amount of magnesium that reacted can be calculated as:
Amount of magnesium reacted = 0.1675 moles x (1 mole of magnesium / 2 moles of HCl)
= 0.08375 moles
Next, we need to determine the molar mass of magnesium. The molar mass of magnesium is approximately 24.31 g/mol.
Now, we can calculate the mass of magnesium that reacted:
Mass of magnesium reacted = Amount of magnesium reacted x Molar mass of magnesium
= 0.08375 moles x 24.31 g/mol
= 2.033 gram
Finally, we can compute the mass % of magnesium in the sample:
Mass % of magnesium = (Mass of magnesium reacted / Initial mass of impure magnesium) x 100
= (2.033 gram / 5.5 gram) x 100
= 36.88%
Therefore, the mass % of magnesium in the impure sample is approximately 36.88%.
To find the mass percentage of magnesium in the impure sample, we need to calculate the amount of magnesium that reacted with the HCl and compare it to the initial mass of the sample. Here's how we can solve this problem:
1. Calculate the number of moles of magnesium that reacted with the HCl solution:
The given amount of HCl solution is 0.3 L and its concentration is 0.6 M.
So, the number of moles of HCl used is: Moles of HCl = Concentration × Volume
Moles of HCl = 0.6 M × 0.3 L = 0.18 mol
The remaining moles of HCl after the reaction is given as 0.0125 mol.
Therefore, the moles of HCl reacted with magnesium is: Moles of HCl reacted = Initial moles of HCl - Remaining moles of HCl
Moles of HCl reacted = 0.18 mol - 0.0125 mol = 0.1675 mol
2. Calculate the number of moles of magnesium that reacted with the HCl solution:
From the balanced equation of the reaction between magnesium and HCl, we know that 1 mole of magnesium reacts with 2 moles of HCl.
So, Moles of magnesium = 0.5 × Moles of HCl reacted
Moles of magnesium = 0.5 × 0.1675 mol = 0.08375 mol
3. Calculate the mass of magnesium that reacted:
The atomic mass of magnesium (Mg) is approximately 24.31 g/mol.
Mass of magnesium = Moles of magnesium × Atomic mass of magnesium
Mass of magnesium = 0.08375 mol × 24.31 g/mol = 2.022 g
4. Calculate the mass percentage of magnesium in the sample:
The initial mass of the impure sample was given as 5.5 g.
Mass percentage of magnesium = (Mass of magnesium / Initial mass of sample) × 100%
Mass percentage of magnesium = (2.022 g / 5.5 g) × 100% = 36.76%
Therefore, the mass percentage of magnesium in the impure sample is approximately 36.76%.