What mass of limestone (in kg) would be required to completely neutralize a 15.2 billion-liter lake that is 1.9×10−5 M in sulfuric acid and 8.6×10−6 M in nitric acid?
Well, let's calculate it step by step! First, we need to determine the moles of sulfuric acid (H2SO4) and nitric acid (HNO3) in the lake.
To find the moles of sulfuric acid:
Moles of H2SO4 in the lake = concentration of H2SO4 x volume of the lake
= (1.9×10^-5 mol/L) x (15.2 x 10^9 L)
To find the moles of nitric acid:
Moles of HNO3 in the lake = concentration of HNO3 x volume of the lake
= (8.6×10^-6 mol/L) x (15.2 x 10^9 L)
Now, since limestone (CaCO3) reacts with both sulfuric acid and nitric acid based on their stoichiometry, we can calculate the moles of limestone required to neutralize the lake.
The balanced equation for the reaction between limestone and sulfuric acid is:
CaCO3 + H2SO4 → CaSO4 + CO2 + H2O
The balanced equation for the reaction between limestone and nitric acid is:
CaCO3 + 2HNO3 → Ca(NO3)2 + CO2 + H2O
From the balanced equations, we see that one mole of limestone reacts with one mole of either of the acids. Therefore, the moles of limestone required will be the sum of the moles of sulfuric acid and nitric acid.
Total moles of limestone required = Moles of H2SO4 + Moles of HNO3
= (Moles of H2SO4 in the lake) + (Moles of HNO3 in the lake)
We can find the mass of limestone required using the molar mass of CaCO3:
Mass (in kg) of limestone required = Total moles of limestone required x Molar mass of CaCO3
Finally, we have our answer! However, I must admit, the calculation got a bit serious and scientific. But hey, at least it wasn't as boring as watching paint dry, right?
To calculate the mass of limestone required to neutralize the lake, we need to determine the amount of acid present and then use stoichiometry to find the mass of limestone.
Here's the step-by-step approach to get the answer:
Step 1: Determine the moles of sulfuric acid and nitric acid in the lake.
To do this, we need to calculate the total volume of the lake and then use the given concentrations (Molarity) of the acids.
Given:
- Volume of the lake = 15.2 billion liters = 15.2 x 10^9 L
- Concentration of sulfuric acid = 1.9 × 10^(-5) M
- Concentration of nitric acid = 8.6 × 10^(-6) M
Using the formula:
moles = concentration x volume (in liters)
For sulfuric acid:
moles of sulfuric acid = (1.9 × 10^(-5) M) x (15.2 x 10^9 L)
For nitric acid:
moles of nitric acid = (8.6 × 10^(-6) M) x (15.2 x 10^9 L)
Step 2: Determine the stoichiometry between the acid and the limestone.
The balanced chemical equation for the reaction between limestone (calcium carbonate) and sulfuric acid is:
CaCO₃ + H₂SO₄ → CaSO₄ + CO₂ + H₂O
1 mole of CaCO₃ reacts with 1 mole of H₂SO₄
Similarly, the balanced chemical equation for the reaction between limestone and nitric acid is:
CaCO₃ + 2HNO₃ → Ca(NO₃)₂ + CO₂ + H₂O
1 mole of CaCO₃ reacts with 2 moles of HNO₃
Step 3: Calculate the moles of CaCO₃ required to neutralize the acids.
Since 1 mole of CaCO₃ reacts with 1 mole of H₂SO₄ and 1 mole of CaCO₃ reacts with 2 moles of HNO₃, we can calculate the moles of CaCO₃ required for each acid separately.
moles of CaCO₃ required for sulfuric acid = moles of sulfuric acid
moles of CaCO₃ required for nitric acid = 2 x moles of nitric acid
Step 4: Calculate the total moles of CaCO₃ required.
To get the total moles of CaCO₃ needed, we add the moles of CaCO₃ required for sulfuric acid and nitric acid.
Total moles of CaCO₃ = moles of CaCO₃ required for sulfuric acid + moles of CaCO₃ required for nitric acid
Step 5: Determine the molar mass of CaCO₃.
Calcium carbonate (CaCO₃) has a molar mass of:
Ca = 40.08 g/mol
C = 12.01 g/mol
O = 16.00 g/mol (x3)
Calculate the molar mass:
Molar mass of CaCO₃ = (40.08 g/mol) + (12.01 g/mol) + (16.00 g/mol x 3)
Step 6: Calculate the mass of CaCO₃ required.
To get the mass of CaCO₃ required, use the following formula:
Mass = moles x molar mass
Mass of CaCO₃ required = Total moles of CaCO₃ x Molar mass of CaCO₃
Now, plug in the values calculated from the previous steps into the formula to find the mass of limestone required to neutralize the lake.
For the sulfuric acid..
moles limestone=moles acid
for the nitric acid,
moles limestone=2*moles nitric acid
I will be happy to check your calculations