Question

Question #90f5f

Answer 1

The final pressure will be `"7.40 atm"`.

Explanation:

The Combined Gas Law can be used to answer this question. It states that the volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure. The equation is:

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

At STP, the standard temperature is `0^@"C"` or `"273.15 K"`. With gas laws, the Kelvin temperature is used. The standard pressure can vary, but since you need the answer in atmospheres, it will be `"1 atm"`. (The more current standard pressure is `"10"^5color(white)(.) "Pa"`, or `"100 kPa"`, or `"1 bar"`, all of which are equal.

To convert `""^@"C"` to Kelvins, add `273.15` to the Celsius temperature.

Organize your data:

Given
`P_1="1 atm"`
`V_1="0.500 L"`
`T_1="273.15 K"`
`V_2=7.50xx10^(-2)color(white)(.)"L"="0.0750 L"`
`T_2="30"^@"C"+273.15="303 K"`

Unknown: `P_2`

Solution
Rearrange the equation to isolate `P_2` and insert the given data into the equation, then solve.

`P_2=(P_1V_1T_2)/(T_1V_2)`

`P_2=(1"atm"xx0.500color(red)cancel(color(black)("L"))xx303color(red)cancel(color(black)("K")))/(273.15color(red)cancel(color(black)("K"))xx0.0750color(red)cancel(color(black)("L")))="7.40 atm"` rounded to three significant figures

Answer 2

`"739.7 kPa"`

Explanation:

The gas law states that `PV=nRT`.

In the first part of the question, you are told that the gas occupies `"0.500 L"` at standard temperature and pressure.
this means that conditions are:

• `"273.15 Kelvin"` (0 celsius)
• `"100,000 Pascals"` of pressure
• `"0.500 L"` volume (Which corresponds to `"0.0005 m"^3"`)
  The `R` in the gas law is the Molar gas constant, this value is `"8.314 m"^3 "Pa K"^(−1) "mol"^(−1)"` .

With this information, you can calculate the number of moles of gas you have in your sample.

`PV=nRT`

`n=(PV)/RT`

`n=(100,000*0.0005)/(273.15*8.314)`

`"n=0.02201 Moles"`

With this information, you can now answer the second step. The conditions are now:

• `"303.15 Kelvin"`
• `"0.075 L"` (which corresponds to `"0.000075 m"^3"`)
  -`"0.02201 Moles"`
  Now the equation is re-arranged to `P=(nRT)/V`

`P=(0.02201*8.314*303.15)/(0.000075)`

`P="739650.19 Pa"`

The final pressure is `"739650 Pascals"` or `"739.7 kPa"`. This is `"7.30 atm"`.

Hope this helped :D