1. An argon gas occupies 50 L at 760 torr. If the volume of gas is decreased to ½ of the original volume, calculate its final pressure. 2. At 0°C and 5 atm, a given sample of gas occupies 65 L. The gas is compressed to a final volume of 10 L at 0°C. What is the final pressure?
Answer (1)
1. Argon Gas (Boyle's Law)Formula: > P₁ × V₁ = P₂ × V₂Where:P₁ = initial pressureV₁ = initial volumeP₂ = final pressureV₂ = final volumeGiven:P₁ = 760 torrV₁ = 50 LV₂ = ½ × 50 = 25 LFind P₂Solution:[tex] \bold{P_2 = \frac{P_1 \times V_1}{V_2} = \frac{760 \times 50}{25} = \boxed{ \bold{1520 \: torr}}}[/tex]Answer: 1520 torr2. Gas Compressed (Combined Gas Law)Formula: > Since final pressure is missing, we use this formula: P₂ = P1T2V1 over T1V2Where:P₁ = initial pressureV₁ = initial volumeT1 = initial temp.P₂ = final pressureV₂ = final volumeT2 = final tempGiven:P₁ = 5 atmV₁ = 65 LV₂ = 10 LT1 is constant (273°K)T2 is constant (273°K)Find P₂Solution:[tex] \bold{P_2 = \frac{P_1 \times T_2 \times V_1}{T_1 \times V_2} = \frac{5 \times 273 \times 65}{273 \times 10} = \boxed{ \bold{32.5 \: atm}}}[/tex]Answer: 32.5 atm
