Calculate the volume of 1.78M sulfuric acid that would be needed to neutralize 62.4 mL of a 2.09 M aqueous ammonia solution. The equation for the reaction is
H2SO4(aq) + 2 NH3(aq) ---> 2 NH4(aq)+ SO4
^-2 (aq)
How much NH3 do you have? That is mols = M x L = ?
Look at the coefficients in the balanced equation. It takes 1/2 as much H2SO4. So mols H2SO4 = 1/2 mols NH3.
M H2SO4 = mols H2SO4/L H2SO4.
You know M and mols, solve for L.
To calculate the volume of sulfuric acid needed to neutralize the aqueous ammonia solution, we can use the concept of stoichiometry.
First, we need to determine the balanced equation for the reaction between sulfuric acid and ammonia. The given equation is not balanced correctly, so let's balance it:
H2SO4(aq) + 2 NH3(aq) → 2 NH4+(aq) + SO4^2-(aq)
Now we can see that according to the balanced equation, 1 mole of sulfuric acid reacts with 2 moles of ammonia to produce 2 moles of ammonium ions and 1 mole of sulfate ions.
Given:
- Volume of sulfuric acid solution: Not provided. We need to calculate it.
- Concentration of sulfuric acid solution: 1.78 M
- Volume of aqueous ammonia solution: 62.4 mL
- Concentration of aqueous ammonia solution: 2.09 M
To solve the problem, we need to follow these steps:
Step 1: Convert the volume of aqueous ammonia to moles.
We use the equation: Moles = Molarity × Volume (in liters)
Moles of NH3 = 2.09 M × (62.4 mL / 1000 mL/L) = 0.130416 moles
Step 2: Use the stoichiometry of the balanced equation to find the moles of sulfuric acid.
From the balanced equation, we see that 2 moles of NH3 react with 1 mole of H2SO4.
Therefore, Moles of H2SO4 = 0.130416 moles / 2 = 0.065208 moles
Step 3: Convert the moles of sulfuric acid to volume (in liters) using the molarity.
Volume of H2SO4 = Moles / Molarity = 0.065208 moles / 1.78 M = 0.036644 liters
To convert the volume to milliliters, we multiply by 1000:
Volume of H2SO4 = 0.036644 liters × 1000 mL/L = 36.644 mL
Therefore, the volume of 1.78 M sulfuric acid needed to neutralize 62.4 mL of a 2.09 M aqueous ammonia solution is approximately 36.644 mL.