Question

A researcher studying ozone (O3) fills a plastic bag with ozone and finds that it contains 2.01g of ozone and has a volume of 0.938L. The bag is then filled with additional ozone to make a volume of 2.34L at the same temperature and pressure. How many grams of ozone are now in the bag? The molar mass of ozone is 47.997 g/mol.

Answer 1

Answer: The mass of ozone present in the bag now is 50.16 grams

Step-by-step explanation:

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}` .....(1)

Given mass of ozone = 2.01 g

Molar mass of ozone = 47.997 g/mol

Putting values in equation 1, we get:

`\text{Moles of ozone}=(2.01g)/(47.997g/mol)=0.419mol`

The relationship of number of moles and volume at constant temperature and pressure was given by Avogadro's law. This law states that volume is directly proportional to number of moles at constant temperature and pressure.

The equation used to calculate number of moles is given by:

`(V_1)/(n_1)=(V_2)/(n_2)`

where,

`V_1\text{ and }n_1` are the initial volume and number of moles

`V_2\text{ and }n_2` are the final volume and number of moles

We are given:

`V_1=0.938L\\n_1=0.419mol\\V_2=2.34L\\n_2=?`

Putting values in above equation, we get:

`(0.938)/(0.419)=(2.34)/(n_2)\\\\n_2=(2.34* 0.419)/(0.938)=1.045mol`

Now, calculating the mass of ozone from equation 1, we get:

Molar mass of ozone = 47.997 g/mol

Moles of ozone = 1.045 moles

Putting values in equation 1, we get:

`1.045mol=\frac{\text{Mass of ozone}}{47.997g/mol}\\\\\text{Mass of ozone}=(1.045mol* 47.997g/mol)=50.16g`

Hence, the mass of ozone present in the bag now is 50.16 grams