Question

If 20 mL of gas is subjected to a temperature change from 10°C to 100°C and a pressure change from 1 atm to 10 atm, the new volume to the correct number of significant digits is: 3 mL 2 mL 24 mL 13 mL none of these choices

Answer 1

First you want to convert the Celsius to Kelvin, so 10C will be 283.15K, and 100C will be 373.15K.

Then, we have to look at the PVnT relationships to determine what to do. Since T increases, that must mean V increases. And since pressure increases, V will increase from that too. I believe it can be assumed # of particles then stay constant.


1) The first ratio is your given value
20mL
———
1
2) you multiply the above by the ratio which favors the relationships: so if the given value is supposed to rise, then the bigger number should be on top, and vice versa. Since no info on # particles is included, that’ll be excluded.
.... 373.15K x 10atm
———— ————
283.15K 1 atm


So 1) multiplied by 2) gives 263.57 mL, which means the answer is none of the choices.

Answer 2

Answer: Therefore, the final volume of the gas will be 3 ml.

Explanation: Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

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

where,

`P_1` = initial pressure of gas = 1 atm

`P_2` = final pressure of gas = 10 atm

`V_1` = initial volume of gas = 20 ml

`V_2` = final volume of gas = ?

`T_1` = initial temperature of gas =
`10^oC=273+10=283K`

`T_2` = final temperature of gas =
`100^oC=273+100=373K`

Now put all the given values in the above equation, we get the final pressure of gas.

`(1atm* 20ml)/(283K)=(10atm* V_2)/(373K)`

`V_2=3ml`

The answer must contain the same number of significant digits as contained in the least precise term.

Therefore, the final volume of the gas will be 3 ml.