Question

Brine has a density of $1.2g/cc$ . $40cc$ of it is mixed with $30cc$ of water. The density of the solution is:
a. $2.11g/cc$
b. $1.11g/cc$
c. $12.2g/cc$
d. $20.4g/cc$

Answer 1

Hint: The volume of the mixture is the sum of the individual volumes and density is the ratio of mass and volume. Use these along with the given information of the mixture. This will help to find equations between the unknown densities. Solve the equations to find densities.

Complete step by step answer:
The density of Brine say ${\rho _b} = 1.2g/cc$
The volume of Brine say ${V_b} = 40cc$
Since mass is equal to the product of density and volume.
Therefore, the Mass of Brine is
${m_b} = {\rho _b} \times {V_b}$
$ \Rightarrow {m_b} = 1.2 \times 40 = 48g$
As we know the density of the water is ${\rho _w} = 1g/cc$
The volume of water say ${V_b} = 30cc$
Mass of water $ = {m_w} = {\rho _w} \times {V_b}$
$ \Rightarrow {m_w} = 1 \times 30 = 30g$
Since the Formula of density is,
Density of mixture $ = {\rho _M} = \dfrac{{{m_b} + {m_w}}}{{{V_b} + {V_w}}}$
$ \Rightarrow {\rho _M} = \dfrac{{48 + 30}}{{40 + 30}}$
$ \Rightarrow {\rho _M} = \dfrac{{78}}{{70}} = 1.11g/cc$.

Hence, the correct answer is option (B).

Additional information:
When two liquids of two different densities are mixed, they separate when we stop mixing them. The heavier liquid goes to the bottom as the density is high and the lighter liquid will deposit at the top layer as its density is less. The densest liquid is molasses and the least dense is alcohol. The density of the final mixture after mixing different liquids with different densities will be the relation between the total mass of the liquids and the total volume occupied by the liquids. After settling down, we will observe that the least dense liquid will stay on top and the densest one at the bottom.

Note: If two liquids have the same volume, it doesn’t mean they have the same density. The density is equal to the mass by the volume. So, if the masses of the liquids are also the same, then we can say the densities of the liquids are the same. In the above question, we found the mass of the liquid in known terms only.