Question 1.38 - Chemistry: Molecular Nature Of Matter And Change

Question

An empty vial weighs . (a) If the vial weighs  when filled with liquid mercury (d = 13.53g/cm³ ), what is its volume? (b) How much would the vial weigh if it were filled with water ( $\mathbf{d}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{997}\mathbf{ }\mathbf{g}\mathbf{/}{\mathbf{cm}}^{\mathbf{3}}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{25}\mathbf{°}\mathbf{C}$ )?

Step-by-Step Solution

Answer

Answer

 

(a) The volume of liquid mercury is 9.626cm³ .

(b) The mass of the vial filled with water is 64.92g .

Calculate the volume of liquid mercury

 The given mass of the empty vial is 55.2g .

The total mass of the empty vial and liquid mercury is given as 185.56g  .

The given density of liquid mercury is 13.53g/cm³  .

$$\begin{gathered} The mass of liquid mercury can be calculated by subtracting the mass of the empty vial from the total mass as shown below: \\ Mass of liquid Mercury = toal mass - mass of empty vial \\ = 185.56g - 55.32g \\ = 130.24g \\ \mathrm{The} \mathrm{mass} \mathrm{of} \mathrm{liquid} \mathrm{mercury} \mathrm{is} 130.4\mathrm{g}. \\ \mathrm{The} \mathrm{volume} \mathrm{of} \mathrm{liquid} \mathrm{mercury} \mathrm{can} \mathrm{be} \mathrm{calculated} \mathrm{by} \mathrm{using} \mathrm{the} \mathrm{density} \mathrm{equation} \mathrm{as} \mathrm{follows}: \\ Volume of liquid Mercury =\frac{Mass of liquid mercury}{Density of liquid mercury} \\ = \frac{130.4\mathrm{g}}{13.53g/c{m}^3} \\ = 9.926 c{m}^3 \\ \mathrm{Hence}, \mathrm{the} \mathrm{volume} \mathrm{of} \mathrm{liquid} \mathrm{mercury} \mathrm{in} \mathrm{the} \mathrm{vial} \mathrm{is} 9.926 {\mathrm{cm}}^3. \end{gathered}$$

Determine the mass of the vial when it is filled with water.

The given mass of the empty vial is 55,32g  .

The given density of water is  0.997g/cm³.

 

The volume of water is the same as the volume of liquid mercury. Hence, the volume of water is 9.626 cm³ .

 

Use the below equation to calculate the mass of water in the vial.

$$\begin{gathered} Mass of water = Density of water \times volume of water \\ = 0.997g/c{m}^3 \times 9.626 c{m}^3 \\ =9.597g \end{gathered}$$

The mass of the vial when it is filled with water can be determined as follows:

$$\begin{gathered} Massf vial filled with water = mass of water + mass of empty vial \\ = 9.597g + 55.32g \\ = 64.92g \end{gathered}$$

Therefore, the mass of the vial filled with water is  64.92g.