Question #90f5f

2 Answers
May 8, 2017

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

May 8, 2017

"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