A flask contains 155 cm3 of hydrogen at a pressure of 22.5 kPa. Under what pressure would the gas have a volume of 90.0 cm3 at the same temperature? (Recall that 1 cm3 = 1 mL.)
Answers
Answer:
Before doing any calculations, try to predict what you expect the required pressure to be relative to the given pressure of
22.5 kPa
.
As you know, pressure and volume have an inverse relationship when temperature and number of moles are kept constant - this is known as Boyle's Law.
Simply put, when volume increases, the pressure exerted by the gas molecules decreases. Likewise, when volume decreases, the pressure exerted by the gas molecules increases.
In your case, you want to know what pressure would have resulted in a smaller volume of hydrogen gas. Well, in order for the volume to be smaller, you'd need to have a higher pressure.
You can thus expect the required pressure to be lower than the given
22.5 kPa
.
Explanation:
Mathematically, Boyle's Law is expressed like this
P
1
V
1
=
P
2
V
2
, where
P
1
,
V
1
- the pressure and volume of the gas at an initial state
P
2
,
V
2
- the pressure and volume of the gas at a final state
Rearrange the equation to solve for
P
2
P
2
=
V
1
V
2
⋅
P
1
Plug in your values to get
P
2
=
155
cm
3
90.0
cm
3
⋅
22.5 kPa
=
38.8 kPa
The answer is rounded to three sig figs.
So, the same number of moles of hydrogen gas kept at the same temperature will occupy a volume of
155 cm
3
at a pressure of
22.5 kPa
and a volume of
90.0 cm
3
at a pressure of
38.8 kPa
.