Question

Question #5a3fa

Answer 1

2000K
(non rounded: 1638K)

Explanation:

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

The conditions of STP for gases is 0˚ C and 1 atm

We need to convert our units for the equation written above to be applicable.

`P_1`-- 1 atm
`V_1`-- 0.03 Liters
`T_1`-- 273 Kelvin, 0˚C + 273= Kelvin

`P_2`-- 3 atm: 1 atm = 760 mmHg `(2280mmHg)/760= 3 atm`
`V_2`-- 0.06 Liters
`T_2`-- We will solve for this as a variable

`[.03xx 1]/273=[3 xx 0.06)/x` Now just finish this through simple algebra to get 1638 K

There is 1 significant digit in the rounded version (since 30 and 60 ml have 1 sig fig), Final Answer: 2000K

Answer 2

Use the combined gas law for this question.

The final temperature will be`~~"2000 K"`.

Explanation:

There are three variables in this question, volume `(V)`, temperature `(T)`, and pressure `(P)`. These variables represent the combined gas law . The equation is:

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

where `P_1` is the initial pressure in kilopascals (kPa), `V_1` is the initial volume, `T_1` is the initial temperature in Kelvins, `P_2` is the final pressure in kPa, `V_2` is the final volume, and `T_2` is the final temperature in Kelvins.

As you can see, we will need to make some conversions of the units for the variables.

STP
STP is currently `0^@"C"`, or `"273.15 K"` for gas laws. Pressure is `"10^5 Pa"` or `"100 kPa"`. The pressure needs to be converted from `"mmHg"` to `"kPa"`.

List what is known/given:
`P_1="100 kPa"`
`V_1="30 mL"`
`T_1="273.15 K"`
`P_2=2280color(red)cancel(color(black)("mmHg"))xx(1 "kPa")/(7.50061561303color(red)cancel(color(black)("mmHg")))="303.9750492 kPa"`
`V_2="60 mL"`

List what is unknown: `T_2`

Solution
Rearrange the combined gas law to isolate `T_2`. Substitute the known values into the equation and solve.

`T_2=(P_2V_2T_1)/(P_1V_1)`

`T_2=(303.9750492color(red)cancel(color(black)("kPa"))xx60color(red)cancel(color(black)("mL"))xx273.15"K")/(100color(red)cancel(color(black)("kPa"))xx30color(red)cancel(color(black)("mL")))="2000 K"` rounded to one significant figure