how many milliliters of concentrated H2SO4 of density 1.84 containing 95.6% by weight of the acid is required to prepare 5litres of battery acid of density 1.18 containing 25.2% by weight of acid?
To calculate the required milliliters of concentrated H2SO4, we can set up a proportion using the given information.
Let's assume:
x = milliliters of concentrated H2SO4 needed
Step 1: Calculate the mass of the battery acid required.
Given:
Volume of battery acid = 5 liters
Density of battery acid = 1.18 g/mL
Percentage of acid in battery acid = 25.2% (by weight)
Mass of battery acid = volume × density
Mass of battery acid = 5 liters × 1.18 g/mL
Mass of battery acid = 5 × 1000 mL × 1.18 g/mL
Mass of battery acid = 5900 grams
Step 2: Calculate the mass of the acid in the battery acid.
Mass of acid in battery acid = percentage of acid × mass of battery acid
Mass of acid in battery acid = 25.2% × 5900 grams
Mass of acid in battery acid = 1486.8 grams
Step 3: Calculate the required milliliters of concentrated H2SO4.
Given:
Density of concentrated H2SO4 = 1.84 g/mL
Percentage of acid in concentrated H2SO4 = 95.6% (by weight)
Mass of acid in concentrated H2SO4 = percentage of acid × mass of concentrated H2SO4
Mass of acid in concentrated H2SO4 = 95.6% × x mL × 1.84 g/mL
Now, we can set up a proportion:
Mass of acid in concentrated H2SO4 / Mass of acid in battery acid = Volume of concentrated H2SO4 / Volume of battery acid
(95.6% × x mL × 1.84 g/mL) / 1486.8 grams = x mL / 5000 mL
Simplifying the equation:
(0.956 × 1.84) / 1486.8 = x / 5000
0.95 / 1486.8 = x / 5000
Cross-multiplying:
x = (0.95 / 1486.8) × 5000
x ≈ 3.19 mL
Therefore, approximately 3.19 milliliters of concentrated H2SO4 are required to prepare 5 liters of battery acid.