A simple of orgen (as) han Of 760 forr. Data a volume of 3.0 L at an initional pressure The same amount of gas at the same temperature was transferred. to a 120 L Container. What 2.) A is the a pressure pressure the oxygen gas (0s) in the new container. gas tank can hold 25.0 I of helium (He) gas at a of 6.0 atm. How many liters will the gas occupy if the pressure was decreased to oso atm at constant σε 3.) A gas is an environment that has temperature? a volume of 16.8L and a pressure of 3.2 atm. If the volume charges to 10. CL, What will be the new pressure? 4.) A gas occupies 15.3 liters at a pressure of 60 mmHg. What is the volume when the pressure is increased to 800 mmity.
Answer (1)
Answer:These problems all involve the Ideal Gas Law, or variations of it, assuming constant temperature. The Ideal Gas Law is: PV = nRT, where: - P = pressure - V = volume - n = number of moles of gas - R = ideal gas constant - T = temperature Since the amount of gas (n) and temperature (T) remain constant in each problem, we can simplify the Ideal Gas Law to: P₁V₁ = P₂V₂ where the subscripts 1 and 2 represent the initial and final conditions, respectively. Let's solve each problem: 1. Oxygen Gas Transfer: - P₁ = 760 torr - V₁ = 3.0 L - P₂ = ? - V₂ = 12.0 L P₁V₁ = P₂V₂760 torr * 3.0 L = P₂ * 12.0 LP₂ = (760 torr * 3.0 L) / 12.0 LP₂ = 190 torr The pressure of the oxygen gas in the new container is 190 torr. 2. Helium Gas Compression: - V₁ = 25.0 L - P₁ = 6.0 atm - V₂ = ? - P₂ = 0.50 atm P₁V₁ = P₂V₂6.0 atm * 25.0 L = 0.50 atm * V₂V₂ = (6.0 atm * 25.0 L) / 0.50 atmV₂ = 300 L The helium gas will occupy 300 liters. 3. Gas Volume Change: - V₁ = 16.8 L - P₁ = 3.2 atm - V₂ = 10.0 L - P₂ = ? P₁V₁ = P₂V₂3.2 atm * 16.8 L = P₂ * 10.0 LP₂ = (3.2 atm * 16.8 L) / 10.0 LP₂ = 5.376 atm The new pressure will be approximately 5.4 atm. 4. Gas Pressure Change: - V₁ = 15.3 L - P₁ = 60 mmHg - V₂ = ? - P₂ = 800 mmHg P₁V₁ = P₂V₂60 mmHg * 15.3 L = 800 mmHg * V₂V₂ = (60 mmHg * 15.3 L) / 800 mmHgV₂ = 1.1475 L The volume will be approximately 1.1 L. Remember to always check your units for consistency. In problem 2, I assumed the units for pressure were atmospheres (atm) and the units for volume were liters (L). If different units were given, you would need to convert them to be consistent before applying the formula.
