7.) a syringe initially holds a sample of gas with a volume of 285 ml at 355 k and 1.88 atm. to
what temperature must the gas in the syringe be heated/cooled in order to have a volume of 435
ml at 2.50 atm?
a) 139 k
b) 572 k
c) 175 k
d) 466 k
e) 721 k

T₂ = 721 k

Explanation:

Given data:

Initial volume = 285 mL

Initial pressure = 1.88 atm

Initial temperature = 355 K

Final temperature = ?

Final volume = 435 mL

Final pressure = 2.50 atm

Formula:  

P₁V₁/T₁ = P₂V₂/T₂  

P₁ = Initial pressure

V₁ = Initial volume

T₁ = Initial temperature

P₂ = Final pressure

V₂ = Final volume

T₂ = Final temperature

Solution:

P₁V₁/T₁ = P₂V₂/T₂  

T₂  =  P₂V₂ T₁  / P₁V₁

T₂ = 2.50 atm × 435 mL × 355 K / 1.88 atm × 285 mL  

T₂ = 386062.5 atm. mL. K /535.8 atm. mL

T₂ = 721 k