Question

A flask with a sample of gas at room temperature and pressure weighs 97.4842 g. The same flask with air (density = 1.17 g/L) weighs 96.8848 g. The same flask filled with water (d = 0.998 g/mL) weighs 345.86 g. The pressure in the room is 0.989 atm and the temperature is 22.2 °C.

1. Calculate the volume of the flask.

2. Calculate the mass of the air that the flask can hold.

3. Calculate the mass of the empty (no air) flask.

4. Calculate the mass of the gas in the flask.

5. Use the Ideal gas law to calculate the moles of gas in the flask.

6. Calculate the molar mass of the gas in the flask.

Answer 1

We can calculate the volume of flask after calculating the mass of gas and/ or mass of water in the flask. As volume of flask will be equal to volume of gas or volume of water in the flask.

Let the mass of flask be x g.

Also let m_air represent mass of air, and m_water represent mass of water in the flask.

Then, m_air + x =96.8848 g ---------------(i)

m_water + x = 345 .86 g ------------(ii)

Therefore, x = 96.8848 g -   m_air

  x =   345 .86 g - m_water

Equating the above equations, we get

96.8848 g -   m_air = 345 .86 g - m_water -----------------------(iii)

Also , volume of air = volume of water = volume of flask = V mL

Density of air = 1.17 g / L= 0.00117 g / mL -----[ 1 L = 1000 mL]

Density of air = m_air / V

V = m_air / Density of air

V=  m_air / 0.00117 g mL^-1

Density of water  = 0.998 g mL^-1

^Therefore,

V= m_water /    0.998 g mL^-1

Equating the two volumes , we get

m_air / 0.00117 g mL^-1 =  m_water /    0.998 g mL^-1

  m_water = 852.99 m_air ----------------------(iv)

Substituting m_water value from equation (iv) in equation (iii), we get

96.8848 g -   m_air = 345 .86 g - m_water

96.8848 g -   m_air = 345 .86 g - 852.99 m_air

851.99 m_air = 248.9752

m_air = 0.2922 g

Substituting for m_air in equation (iv) to get  m_water,

  m_water = 852.99 m_air

   =852.99 * 0.2922 g

  m_water = 249.267 g   

Substituting for m_air in equation (i) to get mass of flask

m_air + x =96.8848 g

0.2922 g + x = 96.8848 g

x = 96.592 g

Therefore, mass of flask =96.592 g

Now we can answer the given questions,

1. Volume of flask = Volume of air in flask = Volume of water in flask

Using air to calculate the volume

V = m_air / Density of air

V = 0.2922 g  / 0.00117 g mL^-1 = 249 .74 mL

Therefore, volume of flask = = 249 .74 mL

2. As shown in calculations above

Mass of air that flask can hold = 0.2922 g​​​​​​​

3. As shown in calculations above

Mass of empty flask =96.592 g

4. Mass of gas + mass of flask = 97.4842 g

Mass of gas = 97.4842 g -mass of flask

= 97.4842 g - 96.592 g

= 0.8922 g

5. Using ideal gas law

PV= nRT

n= PV / RT

We have,

Volume of gas = volume of flask =249 .74 mL = 0.24974 L

Given ,

P = 0.989 atm

T = 22.2  °C = 22.2 +273.15 K = 295.35 K

Using , R = 0.082 L atm K^-1 mol^-1

Plugging these values to find n,

n= PV / RT

= ( 0.989 atm) (0.24974 L) / (0.082 L atm K^-1 mol^-1) ( 295.35 K )

= 0.010198 moles

No. of moles of gas = 0.010198 moles

​​​​​​​

6. Molar mass of gas = Mass of gas in flask / no. of moles of gas

= 0.8922 g / 0.010198 moles

= 87.487 g / mol