Question

Determine which law is appropriate for solving the following problem. What temperature will 215 mL of a gas at 20°C and 1 atm pressure attain when it is subject to 1.5 atm of pressure? what Law is used: Combined gas law, Charles Law, or boyles law?

Answer 1

The Combined Gas Law

Explanation:

Let’s compare the two conditions.

p₁ = 1 atm; V₁ = 215 mL; T₁ = 20 °C

p₂ = 1.5 atm; V₂ = 215 mL; T₂= ?

The only variables are pressure and temperature.

The most appropriate law would be Gay-Lussac’s Law (p₁/T₁ = p₂/T₂), but that’s not an option.

The only other option involving p and T is the Combined Gas Law:

p₁V₁/T₁ = p₂V₂/T₂

Since V₂ = V₁, we can write

p₁V₁/T₁ = p₂V₁/T₂ Divide both sides by V₁

p₁/T₁= p₂/T₂ Multiply both sides by T₂

p₁T₂/T₁ = p₂ Multiply both sides by T₁

p₁T₂= p₂T₁ Divide both sides by p₁

T₂ = T₁ × p₂/p₁

Now, convert your temperature to kelvins, insert the values into the formula, and calculate the new temperature.

Answer 2

Answer : The temperature will be 439.5 K and combined gas law is used.

Solution : Given,

Volume = 215 ml

Initial conditions,

`T_1=20^oC=273+20=293K`
`(0^oC=273K)`

`P_1=1atm`

`P_2=1.5atm`

Using combined gas law,

`(PV)/(T)=constant`

where,

P = pressure of gas

V = volume of gas

T = temperature of gas

As per the problem, at constant volume the combined gas law is expressed as,

`(P_1)/(T_1)=(P_2)/(T_2)`

Now put all the given values in this formula, we get

`(1atm)/(293K)=(1.5atm)/(T_2)`

By rearranging the term, we get the value of
`T_2`.

`T_2=439.5K`

Therefore, the temperature will be 439.5 K and combined gas law is used.