Question

Part A

A syringe containing 1.35 mL of oxygen gas is cooled from 92.8 ∘C to 0.9 ∘C. What is the final volume Vf of oxygen gas?

Part B

A cylinder with a moveable piston contains 0.540 mol of gas and has a volume of 300 mL.

What will its volume be if an additional 0.279 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)

Answer 1

PART A

If we are considering the gas as an ideal gas , it will obey the gas laws .

It has been given that the initial temperatures T₁ = 92.8 ^oC and the final temperature T₂ = 0.9^oC

So, T₁ = 92.8 + 273

= 365.8 K

and T₂ = 0.9 + 273

= 273.9 K

The initial volume is also given which is V₁ = 1.35 mL

and we need to find out the final volume which is V_f = ?

Now we can use Charles law which states that the volume of a fixed mass of gas is directly proportional to the temperature and is expressed as V₁ / T_{1 =} V₂ / T₂

Substituting the values we get 1.35 / 365.8 = V₂ / 273.9

V₂ = ( 1.35 273.9 ) / 365.8

= 1.01 mL

PART B

Here in this question we can use Avogadro’a law which states that under constant temperature and pressure the volume occupied by an ideal gas is directly proportional to the number of moles  present.

It has been given the initial number of moles n_i = 0.540 mol

The  final number of moles (n_{f )}= initial number of moles + moles of gas added

= 0.540 + 0.279

= 0.819 mol

The initia volume of the gas given is 300 mL

We need to find the final volume V_f

By using the expression of Avogadro’s law we can write n / V = a constant

So, V_i / n_i = V_f / n_f

V_f = (V_i n_f ) / n_i

   _{= ( 300   0.819 ) / 0.540}

_{= 455 mL}