To obtain a product with a specific gravity of 1.310, you should mix 4500 mL of a syrup with a specific gravity of 1.350 with 3000 mL of a syrup with a specific gravity of 1.250.
The specific gravity of a substance is the ratio of its density to the density of water. It serves as a measure of a substance's density compared to water. When mixing substances with different specific gravities, the resulting specific gravity of the mixture can be determined using a weighted average approach.
To find the required amount of the syrup with a specific gravity of 1.350, the following formula can be used:
V₁ = [(SG₂ - SGₘ) × V₂]/(SG₁ - SGₘ)
Where:
- V₁ = volume of syrup with SG 1.350
- SG₁ = specific gravity of syrup with SG 1.350
- V₂ = volume of syrup with SG 1.250
- SG₂ = Specific gravity of syrup with SG 1.250
- SGₘ = Specific gravity of the mixture
Using the given values:
V₁ = [(1.250 - 1.310) × 3000]/(1.350 - 1.310)
V₁ = (-0.060 × 3000)/(0.040)
V₁ = -180 × 0.04
V₁ = -4,500 mL
Thus to obtain a product with a specific gravity of 1.310, 4500 mL of a syrup with a specific gravity of 1.350 should be mixed with 3000 mL of a syrup with a specific gravity of 1.250.