Question

A particular flask has a mass of 17.4916 g when empty. When filled with ordinary water at 20.0°c (density = 0.9982 g/ml), the mass of the flask is now 43.9616 g. The density of so-called "heavy water" at 20.0°c is 1.1053 g/ml. What will the mass of the flask be when filled with heavy water at 20.0°c?

Answer 1

The mass of the flask filled with heavy water at $20{\text{ }}^\circ {\text{C}}$ is $\boxed{46.8016{\text{ g}}}$.

Further Explanation:

The formula to calculate the total mass of flask with ordinary water is as follows:

${\text{Total mass of flask}} = {\text{Mass of empty flask}} + {\text{Mass of ordinary water}}$         …… (1)            

Rearrange equation (1) to calculate the mass of ordinary water.

 ${\text{Mass of ordinary water}} = {\text{Total mass of flask}} - {\text{Mass of empty flask}}$          …… (2)              

The total mass of the flask is 43.9616 g.

The mass of ordinary water is 17.4916 g.

Substitute these values in equation (2).

$\begin{aligned}{\text{Mass of ordinary water}} &= {\text{43}}{\text{.9616 g}} - {\text{17}}{\text{.4916 g}}\\&= {\text{26}}{\text{.47 g}}\\\end{aligned}$  

The formula to calculate the density of a substance is as follows:

  ${\text{Density of substance}} = \dfrac{{{\text{Mass of substance}}}}{{{\text{Volume of substance}}}}$                      …… (3)                                      

Rearrange equation (3) to calculate the volume of the substance.

${\text{Volume of substance}} = \dfrac{{{\text{Mass of substance}}}}{{{\text{Density of substance}}}}$                 …… (4)                                          

Substitute 26.47 g for the mass of the substance and 0.9982 g/mL for the volume of the substance in equation (4) to calculate the volume of ordinary water.

$\begin{aligned}{\text{Volume of ordinary water}} &= \frac{{{\text{26}}{\text{.47 g}}}}{{{\text{0}}{\text{.9982 g/mL}}}}\\&= 26.5177{\text{ mL}}\\\end{aligned}$  

Since the flask is filled with ordinary water having volume 26.5177 mL, the capacity of the flask comes out to be 26.5177 mL.

Rearrange equation (3) to calculate the mass of the substance.

${\text{Mass of substance}} = \left( {{\text{Density of substance}}} \right)\left( {{\text{Volume of substance}}} \right)$           …… (5)                  

Substitute 26.5177 mL for the volume of substance and 1.1053 g/mL for the volume of the substance in equation (5) to calculate the mass of heavy water.

 $\begin{aligned}{\text{Mass of heavy water}}& = \left( {{\text{1}}{\text{.1053 g/mL}}} \right)\left( {26.5177{\text{ mL}}} \right)\\&= 29.310{\text{ g}} \\ \end{aligned}$

The formula to calculate the total mass of flask with heavy water is as follows:

${\text{Total mass of flask}} = {\text{Mass of empty flask}} + {\text{Mass of heavy water}}$                       …… (6)

Substitute 17.4916 g for the mass of the empty flask and 29.310 g for the mass of heavy water in equation (6).

$\begin{aligned}{\text{Total mass of flask}}&= 17.4916{\text{ g}} + {\text{29}}{\text{.310 g}}\\&= 46.8016{\text{ g}}\\\end{aligned}$  

Learn more:

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Answer details:

Grade: Middle School

Chapter: Density

Subject: Chemistry

Keywords: density, mass, volume, 46.8016 g, 17.4916 g, 29.310 g, 29.310, 0.9982 g/mL, 1.1053 g/mL.

Answer 2

The mass of the empty flask is 17.4916 g. Now after feeling the ordinary water the mass of the flask is 43.9616 g. Thus the change of weight due to addition of ordinary water is (43.9616 - 17.4916) = 26.47 g.

Now as the density of the ordinary water at 20°C is 0.9982 g/ml, so 26.47 g is equivalent to $\frac{26.47}{0.9982}=26.5177$ mL of water. Thus the capacity of the flask is 26.5177 mL.

Now the density of heavy water is 1.1053 g/mL at 20°C. Thus 26.5177 mL of heavy water is equivalent to (1.1053×26.5177) = 29.310 g.

Thus the total weight of the flask filled with heavy water will be (17.4916 + 29.310) = 46.8016 g at 20°C.