Question

(II) A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

Short answer

The specific gravity of the other fluid is 0.8547.

Step-by-step solution

Understanding the specific gravity of the other fluid

The specific gravity of the other fluid can be expressed as the ratio of the density of the other fluid to the standard water density. It is a dimensionless quantity.

Identification of the given data

The given data can be listed below,

• The mass of the bottle when it is empty, m_{bottle_empty} = 35g.
• The mass of the bottle when it is filled with water, m_{bottle_filled} = 98.44g.
• The mass of the bottle when filled with another fluid is, m_fluid = 89.22g.

Determination of the specific gravity of the other fluid

The specific gravity can be expressed as,

\begin{aligned}S.G=\frac{{{\rho_{{\rm{other fluid}}}}}}{{{\rho_{{\rm{water}}}}}}\\=\frac{{{{\left({\frac{m}{V}}\right)}_{{\rm{otherfluid}}}}}}{{{{\left({\frac{m}{V}}\right)}_{{\rm{water}}}}}}\end{aligned}

Here, ρ_{other fluid} is the density of the other fluid, ρ_water is the density of the water, m_{other fluid} is the mass of the other fluid, V_{other fluid} is the volume of the other fluid, V_wateris the volume of the water, m_wateris the mass of the water.

As the volume of the bottle remains the same, the importance of other fluids and the volume of water are equal and thus cancel each other.

\begin{aligned}S.G=\frac{{{{\left({\frac{V}{V}}\right)}_{{\rm{otherfluid}}}}}}{{\left({\frac{{{m_{{\rm{water}}}}}}{{{m_{{\rm{otherfluid}}}}}}}\right)}}\\=\frac{{{m_{{\rm{otherfluid}}}}}}{{{m_{{\rm{water}}}}}}\\=\frac{{{m_{{\rm{fluid}}}}-{m_{{\rm{bottle\_empty}}}}}}{{{m_{{\rm{bottle\_filled}}}}-{m_{{\rm{bottle\_empty}}}}}}\end{aligned}

Substitute the values in the above equation.

\begin{aligned}S.G=\frac{{89.22{\rm{g}}-35{\rm{g}}}}{{98.44{\rm{g}}-35{\rm{g}}}}\\=0.8547\end{aligned}

Thus, thespecific gravity of the other fluidis0.8547.