Question

A sample of neon gas in a closed vessel occupies 85.0 mL at 25.0 °C. What is its new volume, in mL, if the temperature decreases to –16.0 °C, with P and n constant?

Answer 1

The new volume of the gas is 73.31 mL at -16°C.

Step-by-step explanation:

Boyle's Law:

The pressure of a given mass at a constant temperature of an ideal gas is inversely proportion to its volume.

`P\propto \frac 1V`

Charles' Law:

The volume is directly proportional to the temperature of an ideal gas of a given mass at a constant pressure.

`V\propto T`

Combined two gas laws

`PV\propto T`

`\therefore (P_1V_1)/(T_1)= (P_2V_2)/(T_2)`

Given that,

A sample of neon gas closed vessel occupied 85.0 mL at 25.0°C with constant P and n.

Here
`P_1=P_2`,
`V_1=85.0` mL,
`T_1` =( 25+273)K=298 k

`V_2=`? ,
`T_2`=(-16+273)K=257 k

Since the pressure is constant.

So, the gas equation becomes

`\therefore (V_1)/(T_1)=(V_2)/(T_2)`

Putting the value of
`V_1`,
`T_1` and
`T_2`

`\Rightarrow(85.0)/(298)=(V_2)/(257)`

`\Rightarrow V_2=(85.0* 257)/(298)`

`\Rightarrow V_2= 73.31` mL

The new volume of the gas is 73.31 mL at -16°C.