Chapter 1, Problem 1ASA

Finding the volume of a flask.

A student obtained a clean, dry glass-stoppered flask. She weighed the flask and stopper on an analytical balance and found the total mass to be $34.166\text{g}$. She then filled the flask with water and obtained a mass for the full stoppered flask of $68.090\text{g}$. From these data, and the fact that at the temperature of the laboratory the density of water was $0.9975\text{g}/\text{mL}$, find the volume of the stoppered flask.

a. First we need to obtain the mass of the water in the flask. This is found by recognizing that the mass of a sample is equal to the sum of the masses of its parts. For the filled, stoppered flask:

$\begin{array}{l}\text{Mass of filled stoppered flask}=\text{mass of empty stoppered flask}+\text{mass of water},\\ \text{so mass of water}=\text{mass of filled flask}-\text{mass of empty flask}\end{array}$

$\text{Mass}\text{of}\text{water}=\text{}\text{}\text{}\text{}\text{}\text{}\_\_\_\_\_g-\_\_\_\_\_g=\_\_\_\_\_\_ \text{g}$

Many mass and volume measurements in chemistry are made by the method used in la. This method is called measuring by difference, and is a very useful one.

b. The density of a pure substance is equal to its mass divided by its volume:

$\text{Density}=\frac{\text{mass}}{\text{volume}}$ or $\text{volume}=\frac{\text{mass}}{\text{density}}$

The volume of the flask is equal to the volume of the water it contains. Since we know the mass and density of the water, we can find its volume and that of the flask. Make the necessary calculation.

$\text{Volume}\text{of}\text{water}=\text{volume of flask }=\_\_\_\_\_\_\_ \text{mL}$

Interpretation Introduction

Interpretation:

The volume of the stoppered flask which contains water with density equals to $0.9975\text{g/mL}$ is to be calculated.

Concept introduction:

The division of mass of a substance to its volume is known as density of that substance. The expression that is used to represent the density of any substance is given below.

$\text{Density}=\frac{\text{mass}}{\text{volume}}$

The SI unit of density is $\text{g}/\text{mL}$.

Answer to Problem 1ASA

The volume of the stoppered flask which contains water with density equals to $0.9975\text{g/mL}$ is $34.009\text{mL}$.

Explanation of Solution

The given total mass of empty flask with its stopper is $34.166\text{g}$.

The observed mass of the stoppered flask when it is filled with water is $68.090\text{g}$.

The density of water is $0.9975\text{g/mL}$.

The mass of water

Firstly, the mass of water that is present in the stoppered flask must be calculated.

The mass of the filled stoppered flask is calculated by the expression given below.

$\text{Mass of filled stoppered flask}=\text{mass of empty stoppered flask}+\text{mass of water}$

The above expression is rearranged to calculate the mass of water that is present in the stoppered flask as given below.

$\text{Mass of water}=\text{mass of filled flask}-\text{mass of empty flask}$

Substitute the values of empty flask and filled flask in the above expression.

$\begin{array}{rll}\text{Mass of water}& =& 68.090\text{g}-34.166\text{g}\\ & =& \text{33}\text{.924}\text{g}\end{array}$

Thus, the mass of water is $\text{33}\text{.924}\text{g}$.

The density of any substance is calculated by the expression given below.

$\text{Density}=\frac{\text{mass}}{\text{volume}}$

The above expression is rearranged to calculate the volume of water that is present in the stoppered flask as given below.

$\text{Volume}=\frac{\text{mass}}{\text{density}}$

Substitute the values of mass and density of water in the above expression.

$\begin{array}{rll}\text{Volume}& =& \frac{\text{33}\text{.924}\text{g}}{0.9975\text{g}/\text{mL}}\\ & =& 34.009\text{mL}\end{array}$

So, the volume of water is $34.009\text{mL}$.

As, the volume of flask is equal to the volume of water present in it, therefore, the volume of stoppered flask is also equal to $34.009\text{mL}$.

Conclusion

The volume of the stoppered flask that contains water is $34.009\text{mL}$.