Question

A sample of gas in a flexible container has an initial pressure of 1.60atm.Then the pressure decreases to 1.04atm and the final volume of the gas is 64.1L.The temperature and number of moles of the gas remain constant

Answer 1

To solve this problem, you can use the ideal gas law, which is given by:

�

�

=

�

�

�

PV=nRT

Where:

�

P is the pressure in atmospheres (atm).

�

V is the volume in liters (L).

�

n is the number of moles of gas.

�

R is the ideal gas constant (approximately 0.0821 L·atm/(mol·K) at standard conditions).

�

T is the temperature in Kelvin (K).

Since the temperature and number of moles are constant, we can use the following relationship:

�

1

�

1

=

�

2

�

2

P

1

​

V

1

​

=P

2

​

V

2

​

Where subscripts 1 and 2 represent the initial and final conditions, respectively.

Given:

�

1

=

1.60

atm

P

1

​

=1.60 atm

�

2

=

1.04

atm

P

2

​

=1.04 atm

�

1

=

?

V

1

​

=? (initial volume)

�

2

=

64.1

L

V

2

​

=64.1 L

Now, you can rearrange the equation to solve for

�

1

V

1

​

:

�

1

=

�

2

⋅

�

2

�

1

V

1

​

=

P

1

​

P

2

​

⋅V

2

​

​

Plug in the values:

�

1

=

1.04

 

atm

⋅

64.1

 

L

1.60

 

atm

V

1

​

=

1.60atm

1.04atm⋅64.1L

​

Calculate

�

1

V

1

​

:

�

1

=

66.744

1.60

 

L

≈

41.715

 

L

V

1

​

=

1.60

66.744

​

L≈41.715L

So, the initial volume of the gas (V1) is approximately 41.715 liters.

Step-by-step explanation: