Question

If 4.5 L of antifreeze solution (specific gravity = 0.80) is added to 3.5 L of water to make a 8.0 L mixture, what is the specific gravity of the mixture? Express your answer using two significant figures.

Answer 1

Answer 2

To calculate the specific gravity of the mixture, we need to first determine the total mass of the mixture and then divide it by the mass of an equal volume of water.

Given: Volume of antifreeze solution (V1) = 4.5 L Specific gravity of antifreeze solution (SG1) = 0.80 Volume of water (V2) = 3.5 L Total volume of the mixture (V_total) = 8.0 L

Step 1: Calculate the mass of the antifreeze solution (m1) and the mass of water (m2). m1 = V1 * SG1 = 4.5 L * 0.80 = 3.6 kg (to two significant figures) m2 = V2 * SG_water (Specific gravity of water = 1.00) = 3.5 L * 1.00 = 3.5 kg (to two significant figures)

Step 2: Calculate the total mass of the mixture (m_total). m_total = m1 + m2 = 3.6 kg + 3.5 kg = 7.1 kg (to two significant figures)

Step 3: Calculate the specific gravity of the mixture (SG_mixture). SG_mixture = m_total / V_total = 7.1 kg / 8.0 L = 0.8875 (to four significant figures)

Rounding the specific gravity to two significant figures, the specific gravity of the mixture is approximately 0.89.