Question

fresh A Sailor on a trans-Pacific solo voyage notices one day that if he puts 250 mL of fresh water into a plastic cup weighing 10.0 g, the cup floats in the seawater around his boat with the fresh water inside the cup at exactly the same level as the seawater outside the cup (see sketch at right). Calculate the amount of salt dissolved in each liter of seawater. Be sure your answer has a unit symbol, if needed, and round it to 2 significant digits. You'll need to know that the density of fresh water at the temperature of the sea around the sailor is 0.999 g/cm. You'll also want to remember Archimedes' Principle, that objects float when they displace a mass of water equal to their own mass. X 5 ? Explanation Check

Answer 1

We know that 1mL = 1cm3

so, density of fresh water = 0.999g/cm​​​​​3 = 0.999g/mL

Mass of cup = 10g

Volume of cup = 250mL = 0.250L

According to Archimedes principle

Mass of fresh water + mass of plastic cup = mass of seawater ..........(1)

Note :- mass of seawater will be given as follows

Mass of seawater = mass of fresh water + mass of salt

Hence,

Mass of fresh water + mass of cup = mass of fresh water + mass of salt

Or

mass of cup = mass of salt

mass of salt = 10g

Note:-10 grams of salt is dissolved in a volume equal to the cup, so the volume of 10 grams of salt will be equal to the volume of the cup.

Volume of seawater = 250mL = 0.250L

Density of salt = mass of salt/volume of seawater

Density of salt = (10g)/(0.250g/L)

Density of salt = 40.0g/L

​​​​