Answer:
1. 0.422 atmospheres
2. 633281.25 Pascals
3. (a) Move up
(b) 868 mmHg
4. 868 mmHg
5. 775 mmHg
6. Partial pressure of He is 0.64 atm.
Partial pressure of oxygen is 1.29 atm.
Partial pressure of N is 2.57 atm.
7. 445.72 torr.
Explanation:
1. To convert 321 torr to atmospheres
1 atmosphere = 760 torr
∴ 1 torr = 1/760 atmospheres
Hence, 321 torr = 321 × 1/760 = 321/760 atmospheres = 0.422 atmospheres
2. To convert 6.25 atmospheres to Pascals, we have;
1 atmosphere = 101325 Pascals
∴ 6.25 atmospheres = 6.25 × 101325 Pascals = 633281.25 Pascals
3. (a) Here we have, given that the value of the pressure on the bottle = 830 mmHg, when the valve is opened, the mercury in the open-end arm will move up because the pressure of the gas inside the flask is more than the pressure on the other side of the open-end arm
(b) After the mercury stops moving the difference between the two columns will be the difference between the two pressures, that is 830 mmHg - 745 mmHg = 85 mmHg
4. From the diagram, it is seen that the differenc beteen the two columns is 123 mm, therefore, the pressure in the flask is 123 mmHg more than the external pressure, hence the pressure of the as in the flask = 745 mmHg + 123 mmHg = 868 mmHg
5. Here we have that the height of the mercury in the open-end is less than the height of the mercury on the arm closer to the flask, therefore, the pressure of the gas in the flask = 825 mmHg - 50 mmHg = 775 mmHg
6. Number of moles of He = 1 mole
Number of moles of oxygen, O = 2 mole
Number of moles of nitrogen, N = 4 mole
From Dalton's law of partial pressure we have that, the total pressure of a given mass of gas is equal to the partial pressure of the individual gases
Hence;
Total number of moles = 1 + 2 + 4 = 7 moles
Mole fraction of He = 1/7
Partial pressure of He = 1/7×4.5 = 0.64 atm.
Mole fraction of oxygen, O = 2/7
Partial pressure of oxygen= 2/7×4.5 = 1.29 atm.
Mole fraction of N = 4/7
Partial pressure of N = 4/7×4.5 = 2.57 atm.
7. From Boyle's law
P₁×V₁ = P₂×V₂
Hence;
P₂ = P₁×V₁/V₂
Where:
P₁ = Initial pressure = 2.57 atm
V₁ = Initial volume =1.57 liters
V₂ = New volume = 6.88 liters
P₂ = New pressure = 2.57×1.57/6.88 = 0.59 atm.
To convert 0.59 atm. to torr, we multiply by 760 thus;
0.59 atm. = 0.59 × 760 torr = 445.72 torr.
