Specific Gravity and antifreeze

[mcs117]

Homework Statement

If 5.0L of antifreeze solution (0.8 specific gravity) is mixed with 4L of water to make a 9.0 L mixture. what is the specific gravity of the mixture?

Homework Equations

SG = density of substance / density of water

The Attempt at a Solution

I am confused as in how to gain the density from the substance gravity. Is it given that the density is 1 g/cm^3 for water?

 

[Shooting Star]

Use CGS system -- there the specific gravity is numerically equal to the density in gm/cc.
1 L = 1000 cc = 1000 mL.

 

[Moetasim]

I would approach this problem by first understanding the concept of specific gravity and how it relates to density. Specific gravity is a unitless measure of the density of a substance compared to the density of water. In other words, it is the ratio of the density of the substance to the density of water.

To solve this problem, we can use the formula SG = density of substance / density of water. However, we need to know the density of the antifreeze solution and the water in order to calculate the specific gravity of the mixture.

The specific gravity of the antifreeze solution is given as 0.8. This means that the density of the antifreeze solution is 0.8 times the density of water. We can also assume that the density of water is 1 g/cm^3, as this is a commonly used value for the density of water.

Now, we can use the formula SG = density of substance / density of water to calculate the density of the antifreeze solution. Rearranging the formula, we get density of substance = SG * density of water.

Substituting the values, density of substance = 0.8 * 1 g/cm^3 = 0.8 g/cm^3.

Next, we need to calculate the total volume of the mixture. This can be done by adding the volumes of antifreeze solution (5.0 L) and water (4.0 L), which gives us a total of 9.0 L.

Finally, we can calculate the specific gravity of the mixture using the formula SG = density of mixture / density of water. The density of the mixture can be calculated by dividing the total mass of the mixture by the total volume of the mixture.

The total mass of the mixture can be calculated by multiplying the density of the antifreeze solution by its volume and the density of water by its volume. This gives us a total mass of (0.8 g/cm^3 * 5.0 L) + (1 g/cm^3 * 4.0 L) = 8.0 g/cm^3.

Therefore, the specific gravity of the mixture is SG = (8.0 g/cm^3) / (9.0 L) = 0.89. This means that the density of the mixture is 0.89 times the density of water, which is slightly higher than the density of pure water.

In conclusion