What is the molarity (M) of an HCl solution, 150 ml of which when treated with excess magnesium liberates 3.5 l of H2 gas measured at STP?
I know molarity is Moles, volume, but how does magnesium come into play?
To determine the molarity of the HCl solution, you need to use the information provided about the reaction between HCl and magnesium.
The balanced chemical equation for the reaction between HCl and magnesium is:
2 HCl + Mg → MgCl2 + H2
From the balanced equation, we can see that 2 moles of HCl react to produce 1 mole of H2 gas. Therefore, the number of moles of H2 gas produced can be calculated by converting the given volume of H2 gas to moles.
At STP (standard temperature and pressure), 1 mole of any gas occupies 22.4 liters. So, the given volume of 3.5 liters of H2 gas at STP can be converted to moles as follows:
Number of moles of H2 gas = Volume of H2 gas / Molar volume at STP
= 3.5 L / 22.4 L/mol
≈ 0.156 moles
Since 2 moles of HCl react to produce 1 mole of H2 gas, the number of moles of HCl can be determined by multiplying the number of moles of H2 gas by the stoichiometric coefficient ratio:
Number of moles of HCl = 2 * 0.156 moles
= 0.312 moles
Now, to calculate the molarity (M) of the HCl solution, we divide the number of moles of solute (HCl) by the volume of the solution in liters:
Molarity (M) = Moles of solute / Volume of solution (in liters)
= 0.312 moles / (150 mL / 1000 mL/L)
= 0.312 moles / 0.150 liters
≈ 2.08 M
Therefore, the molarity of the HCl solution is approximately 2.08 M.
To determine the molarity (M) of the HCl solution, we need to first understand the role of magnesium in this reaction.
In this reaction, magnesium (Mg) is reacting with hydrochloric acid (HCl) to produce hydrogen gas (H2) and magnesium chloride (MgCl2). The balanced chemical equation for this reaction is:
Mg (s) + 2HCl (aq) -> MgCl2 (aq) + H2 (g)
The key information provided in the question is the volume of hydrogen gas (H2) liberated, which is 3.5 L at STP (Standard Temperature and Pressure).
Now, let's break down the steps to calculate the molarity of the HCl solution:
Step 1: Calculate the moles of hydrogen gas (H2)
Since we have the volume of H2 gas at STP, we can use the ideal gas law equation to calculate the number of moles of H2:
PV = nRT
At STP, the pressure (P) is 1 atm, the temperature (T) is 273 K and the gas constant (R) is 0.0821 L·atm/mol·K.
n = PV / RT
= (1 atm)(3.5 L) / (0.0821 L·atm/mol·K)(273 K)
= 0.14 mol
Step 2: Calculate the moles of HCl used
From the balanced chemical equation, we can see that 1 mole of Mg reacts with 2 moles of HCl to produce 1 mole of H2. Therefore, the moles of HCl used will be twice the moles of H2 produced.
moles of HCl = 2 × moles of H2
= 2 × 0.14 mol
= 0.28 mol
Step 3: Calculate the molarity (M) of the HCl solution
Molarity (M) is defined as moles of solute divided by the volume of the solution in liters. In this case, the moles of HCl is our solute, and the volume of the HCl solution is given as 150 mL, which is 0.15 L.
Molarity (M) = moles of solute / volume of solution in liters
= 0.28 mol / 0.15 L
= 1.87 M
Therefore, the molarity (M) of the HCl solution is 1.87 M.