Answer:
P
1
V
1
=P
2
V
2
where:
�
1
P
1
and
�
1
V
1
are the initial pressure and volume, respectively.
�
2
P
2
and
�
2
V
2
are the final pressure and volume, respectively.
We can rearrange this equation to solve for
�
2
P
2
:
�
2
=
�
1
�
1
�
2
P
2
=
V
2
P
1
V
1
Now, we'll plug in the values:
�
1
=
262
torr
P
1
=262torr (initial pressure)
�
1
=
21.0
L
V
1
=21.0L (initial volume)
�
2
=
75.0
L
V
2
=75.0L (final volume)
Let's plug these values into the formula to find
�
2
P
2
:
�
2
=
262
torr
×
21.0
L
75.0
L
P
2
=
75.0L
262torr×21.0L
�
2
=
5512
torr
⋅
L
75.0
L
P
2
=
75.0L
5512torr⋅L
�
2
=
73.493
torr
P
2
=73.493torr
Rounded to the appropriate significant figures, the new pressure (
�
2
P
2
) is approximately
73.5
torr
73.5torr.
Step-by-step explanation:
P
1
V
1
=P
2
V
2
where:
�
1
P
1
and
�
1
V
1
are the initial pressure and volume, respectively.
�
2
P
2
and
�
2
V
2
are the final pressure and volume, respectively.
We can rearrange this equation to solve for
�
2
P
2
:
�
2
=
�
1
�
1
�
2
P
2
=
V
2
P
1
V
1
Now, we'll plug in the values:
�
1
=
262
torr
P
1
=262torr (initial pressure)
�
1
=
21.0
L
V
1
=21.0L (initial volume)
�
2
=
75.0
L
V
2
=75.0L (final volume)
Let's plug these values into the formula to find
�
2
P
2
:
�
2
=
262
torr
×
21.0
L
75.0
L
P
2
=
75.0L
262torr×21.0L
�
2
=
5512
torr
⋅
L
75.0
L
P
2
=
75.0L
5512torr⋅L
�
2
=
73.493
torr
P
2
=73.493torr
Rounded to the appropriate significant figures, the new pressure (
�
2
P
2
) is approximately
73.5
torr
73.5torr.