Question

Brine has a density of $1.2g/cc$. $40cc$ of it is mixed with $30cc$ of water. The density of solution is:
A. $2.11g/cc$
B. $1.11g/cc$
C. $12.2g/cc$
D. $20.4g/cc$

Answer 1

We know that the density is defined as the ratio of the mass and volume. Here, we are given the density and the volume of brine. We are also given the volume of the water and the density of water is given by $1g/cc$. From this data, we will first find the mass of both to determine total mass and then we will find the density of solution by using total mass and total volume.

Formula used:
$\rho = \dfrac{m}{V}$
$\rho$ is the density, $m$ is the mass and $V$ is the volume

Complete step by step answer:
First we will find the mass of the brine.Let ${\rho _b}$ be the density, ${m_b}$ is the mass and ${V_b}$ is the volume of the brine. We are given that ${\rho _b} = 1.2g/cc$ and ${V_b} = 40cc$
{\rho _b} = \dfrac{{{m_b}}}{{{V_b}}} \\\ \Rightarrow {m_b} = {\rho _b}{V_b} \\\ \Rightarrow {m_b} = 1.2 \times 40 = 48g \\\
Now, we will find the mass of water.
Let ${\rho _w}$ is the density, ${m_w}$ is the mass and ${V_w}$ is the volume of the water.
We know that ${\rho _w} = 1g/cc$ and it is given that ${V_w} = 30cc$
${\rho _w} = \dfrac{{{m_w}}}{{{V_w}}} \\\ \Rightarrow {m_w} = {\rho _w}{V_w} \\\ \Rightarrow {m_w} = 1 \times 30 = 30g$
Thus, the total mass of solution will be $48 + 30 = 78g$.
Total volume of the solution will be $40 + 30 = 70cc$.
Therefore the total density of the solution is given as the ratio of this total mass and total volume which is $\dfrac{{78}}{{70}} = 1.11g/cc$.

Hence, option B is the right answer.

Note: we have determined the individual mass of brine and water and by adding them and their volume, we have determined the density of the solution. However, we can directly use the formula for the density of the mixture as:
$\rho = \dfrac{{{\rho _b}{V_b} + {\rho _w}{V_w}}}{{{V_b} + {V_w}}} \\\ \Rightarrow \rho = \dfrac{{1.2 \times 40 + 1 \times 30}}{{40 + 30}} \\\ \therefore\rho = 1.11g/cc$