Answer to Question #88663 in General Chemistry for Edidiong Michael inyang

Question

1(a) a vessel containing an unknown volume of argon gas in cm3 at temperature 300f and pressure 101kpa was inverted and placed in cold ethanol. As the gas contracted, the pressure was quadrupled while the temperature reduced by one-third. What is the final volume of gas in dm3?
(B.) Calculate the root mean square of bromine molecule at temperature 23 degree Celsius and at pressure 1.00 atm. What is the root mean square of the same gas at temperature 23 degree Celsius and pressure 1.5 atm

Answer 1

(a) PV = nRT

T₁ = 300 ⁰F = (5/9 x (300 - 32)) + 273 = 422 K;

T₂ = 300/3 = 100 ⁰F = 311 K

P₁ = 101 kPa = 101000 Pa

P₂ = 101 kPa x 4 = 404 kPa = 404000 Pa

P₁V₁ / T₁ = P₂V₂ / T₂

101000 x V₁ / 422 = 404000 x V₂ / 311

V₂ = 0.001 x V₁

 

(b) U_rms = (3p/ρ​)^1/2

1.​ ρ = (p x M) / (R x T);

M(Br₂) = 2 x 80 = 160 g/mol;

R = 0.082 (atm x L)/(mol x K);

T = 23 + 273 = 296 K

ρ = (1 x 160) / (0.082 x 296) = 6.59 g/L;

U_rms = (3 x 1 / 6.59)^1/2​ = 0.4554 m/s

2. ρ = (1.5 x 160) / (0.082 x 296) = 9.89 g/L;

U_rms = (3 x 1,5 / 9.89)^1/2​ = 0.4555 m/s.