Answer to Question #66228 in General Chemistry for Chris

Question

Boyles Law:
Part A
According to Boyle's law, for a fixed quantity of gas at a given temperature, what quantity relating pressure P and volume V is constant?
According to Boyle's law, for a fixed quantity of gas at a given temperature, what quantity relating pressure and volume is constant?
A:PV
B:P×V
C:P+V
D:VP

A 12-liter tank contains helium gas pressurized to 160 atm.
Part B
What size tank would be needed to contain this same amount of helium at atmospheric pressure (1 atm)?
Express the size in liters to three significant figures.

Answer 1

Task 1
Part A
According to Boyle's law, for a fixed quantity of gas at a given temperature, what quantity relating pressure P and volume V is constant?
A:PV
B:P×V
C:P+V
D:VP
Solution:
According to Boyle’s law, for a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure.
That means that, for example, if you double the pressure, you will halve the volume. If you increase the pressure 10 times, the volume will decrease 10 times.
We can express this mathematically as
pV = constant
Thus, answer is A.
Answer: A.
Task 2
A 12-liter tank contains helium gas pressurized to 160 atm.
Part B
What size tank would be needed to contain this same amount of helium at atmospheric pressure (1 atm)?
Express the size in liters to three significant figures.
Solution:
According to Mendeleyev-Klapeyron’s equation, we can calculate the number of moles of Helium gas:
pV = nRT,
where p = 160 atm – pressure; V = 12 l – volume; n – number of moles; R – universal gas constant (R = 0,0821 l∙atm/(mol∙K)); T = 298 K – temperature.
Using given data, we can determine the amount of Helium gas:
n = pV/RT = (160∙12)/(0,0821∙298) = 78,48 (mol)
For atmospheric pressure (1 atm) and the same amount we can calculate the volume of tank, using previous equation:
V = nRT/p = (78,48∙0,0821∙298)/1 = 1920 (liters)
Answer: n = 78,48 moles; V = 1920 liters.