Elementary Question on Relative Density

[John O' Meara]

50g of sulphuric acid of relative density 1.84 are mixed with 50g of water, and the relative density of the mixture is found to be 1.40. Calculate the contraction in volume which has occured? My attempt follows.

R.D., = density of acid/density of water => density of acid =1.84g/cm^3.
A R.D., of 1.40 => a density rho = 1.40g/cm^3.

100g divided by 1.40g/cm^3 = 71.429cm^3.

The contraction in the volume is 28.571cm^3 per 100cm^3 of the mixture!

 

[Curious3141]

50g of sulphuric acid of relative density 1.84 are mixed with 50g of water, and the relative density of the mixture is found to be 1.40. Calculate the contraction in volume which has occured? My attempt follows.

R.D., = density of acid/density of water => density of acid =1.84g/cm^3.
A R.D., of 1.40 => a density rho = 1.40g/cm^3.

100g divided by 1.40g/cm^3 = 71.429cm^3.

The contraction in the volume is 28.571cm^3 per 100cm^3 of the mixture!

What's the initial volume of the dry acid? (It's not 50 cm^3).

 

[kyle8921]

I would first like to clarify that the relative density of a substance is a measure of its density compared to the density of water at a specific temperature. In this case, the relative density of sulphuric acid is 1.84, meaning it is 1.84 times denser than water at the same temperature.

Now, to calculate the contraction in volume, we can use the formula for density, which is mass divided by volume. We know that the total mass of the mixture is 100g, with 50g of sulphuric acid and 50g of water. Using the relative density of the mixture, 1.40, we can calculate the volume of the mixture.

Volume = mass/density = 100g/1.40g/cm^3 = 71.429cm^3

However, this is the volume of the mixture as a whole. To find the contraction in volume, we need to subtract the original volume of the acid (50g/1.84g/cm^3 = 27.174cm^3) from the total volume of the mixture.

Contraction in volume = 71.429cm^3 - 27.174cm^3 = 44.255cm^3

Therefore, the contraction in volume is 44.255cm^3 per 100cm^3 of the mixture. This means that for every 100cm^3 of the mixture, there is a decrease in volume of 44.255cm^3 due to the mixing of the acid and water. I hope this explanation helps to clarify the concept of relative density and how to calculate the contraction in volume.