What volume of 5% vinegar solution is needed to neutralize 1.0g of baking soda if density is 1.01g/ml
To solve this problem, we need to know the molar mass of baking soda (sodium bicarbonate, NaHCO3) and its reaction with vinegar (acetic acid, CH3COOH).
First, let's calculate the molar mass of baking soda:
Na (sodium) = 22.99 g/mol
H (hydrogen) = 1.01 g/mol
C (carbon) = 12.01 g/mol
O (oxygen) = 16.00 g/mol
Total molar mass of baking soda (NaHCO3) = 22.99 + 1.01 + 12.01 + (16.00 × 3) = 84.01 g/mol
Next, let's calculate the number of moles of baking soda in 1.0 g:
moles of baking soda = mass of baking soda / molar mass of baking soda
moles of baking soda = 1.0 g / 84.01 g/mol ≈ 0.0119 mol
According to the balanced chemical equation between baking soda and vinegar, 1 mole of baking soda reacts with 1 mole of vinegar:
NaHCO3 + CH3COOH → NaCH3COO + H2O + CO2
Therefore, the number of moles of vinegar required to neutralize baking soda is also 0.0119 mol.
Now, let's calculate the volume of 5% vinegar solution needed.
First, determine the molarity of the vinegar solution. Since we know the molar mass and density, we can calculate it using the formula:
molarity (M) = moles / volume (L)
Molarity = 0.0119 mol / volume (L)
Since we want to find the volume in milliliters (ml), and density is given in grams per milliliters (g/ml), we can use density to convert to volume:
volume (ml) = mass of vinegar solution (g) / density (g/ml)
Now, we need to find the mass of the vinegar solution. Assuming that the percentage refers to weight per volume:
mass of vinegar solution = mass of vinegar / (percentage / 100)
Since we want a 5% vinegar solution, the mass of vinegar is calculated as follows:
mass of vinegar = 0.05 × mass of vinegar solution
Substituting this equation into the previous formula, we have:
volume (ml) = (0.05 × mass of vinegar solution) / density (g/ml)
To find the volume required to neutralize the baking soda, we need to equate the volume of vinegar solution to 0.0119 mol:
(0.05 × mass of vinegar solution) / density (g/ml) = 0.0119 mol
Rearranging the equation, we get:
mass of vinegar solution = (0.0119 mol × density (g/ml)) / 0.05
Finally, substituting the given density of 1.01 g/ml, we can solve for the mass of vinegar solution:
mass of vinegar solution = (0.0119 mol × 1.01 g/ml) / 0.05 ≈ 0.241 g
Therefore, approximately 0.241 grams of 5% vinegar solution is needed to neutralize 1.0g of baking soda.