A mixture of ALuminum and Zinc weighing 1.67 grams is completely dissolved in hydrochloric acid and 1.750 Liters of hydrogen is produced at 273 Kelvin and 1.0 ATM. can you please help me calculate the mass of Aluminum and Zinc in the Sample?
Sure! To calculate the mass of aluminum and zinc in the sample, we can use the stoichiometry of the reaction between aluminum and zinc with hydrochloric acid.
First, let's write the balanced chemical equation for the reaction:
Al + Zn + 6HCl → 3H2 + AlCl3 + ZnCl2
From the equation, we can see that 2 moles of aluminum react with 1 mole of zinc to produce 3 moles of hydrogen gas. So, the molar ratio of aluminum to zinc is 2:1.
Now, we need to calculate the number of moles of hydrogen gas produced. We can use the ideal gas law equation to do this:
PV = nRT
Where:
P = 1.0 ATM (pressure)
V = 1.750 L (volume)
n = ?
R = 0.0821 L•atm/mol•K (ideal gas constant)
T = 273 K (temperature)
Rearranging the equation to solve for 'n', we have:
n = PV / RT
Plugging in the values, we get:
n = (1.0 ATM) * (1.750 L) / (0.0821 L•atm/mol•K * 273 K)
n ≈ 0.0905 moles
Since the molar ratio of aluminum to zinc is 2:1, we can calculate the number of moles of aluminum and zinc in the sample. Let's assume 'x' moles of aluminum and 'y' moles of zinc.
Then, the mass of aluminum can be calculated as:
Mass of aluminum = x moles * molar mass of aluminum
Similarly, the mass of zinc can be calculated as:
Mass of zinc = y moles * molar mass of zinc
To find the values of 'x' and 'y', we can set up a system of equations:
x + y = 0.0905 (Equation 1)
2x + y = 1.67 (Equation 2)
Solving this system of equations, we find that x ≈ 0.0484 moles and y ≈ 0.0422 moles.
Finally, we can calculate the mass of aluminum and zinc using their respective molar masses. The molar mass of aluminum is 26.98 g/mol, and the molar mass of zinc is 65.38 g/mol.
Mass of aluminum = 0.0484 moles * 26.98 g/mol ≈ 1.31 grams
Mass of zinc = 0.0422 moles * 65.38 g/mol ≈ 2.76 grams
Therefore, the approximate mass of aluminum in the sample is 1.31 grams, and the approximate mass of zinc is 2.76 grams.