i need help please

Question

1)A sample of helium gas has a volume of 303 mL at 0.5 atm. What pressure is needed to reduce the volume at constant temperature to 52 mL? Answer in units of atm.

2)A gas has a pressure of 1.7 atm and occupies a volume of 7.7 L. If the gas is compressed to a volume of 1.08 L, what will its pressure be, assuming constant temperature? Answer in units of atm.

3)A sample of nitrogen gas is contained in a piston with a freely moving cylinder. At 0 ◦C, the volume of the gas is 326 mL. To what temperature must the gas be heated to occupy a volume of 467 mL? Answer in units of ◦C.

4)A helium balloon has a volume of 23.5 L when the pressure is 0.75 atm and the temperature is 18 ◦C. The balloon is cooled at a constant pressure until the temperature is −10◦C. What is the volume of the balloon at this stage? Answer in units of L.

5)The volume of a gas at 27◦C and 0.29 atm is 50 mL. What volume will the same gas sample occupy at standard conditions? Answer in units of mL.

Answer 1

From the ideal gas law, for the same amount n of gas, P₂V₂ / P₁V₁ = T₂ / T₁.

1) At constant T, P₂ = P₁V₁ / V₂ = (0.5 atm) (303 mL) / (52 mL) = 2.9 atm.

2) Likewise, P₂ + (1.7 atm) (7.7 L) / (1.08 L) = 12 atm.

3) At constant P, T₂ = T₁ V₂ / V₁ = (273 K) (467 mL) / (326 mL) = 391 K = 118 °C.

4) Likewise, V₂ = V₁ T₂ / T₁ = (23.5 L) (-10 +273 K) / (18 +273 K) = 21.2 L.

5) All parameters change, V₂ = V₁ P₁ T₂ / P₂ T₁ = (50 mL) (0.29 atm) (273 K) / [(1.00 atm) (27 +273 K) = 13 mL. (STP = 0 °C and 1 atm)