An ideal gas has a volume of 2.28 L at 279 K and 1.07 atm. What is the pressure when the volume is 1.03 L and the temperature is 307 K?

1 Answer
Dec 29, 2015

Answer:

#"p"= 2.61" atm to 3 significant figures"#

Explanation:

First, we use the first set of data to calculate the number of moles using the ideal gas equation:

#"pV " = " nRT"#

Where:

  • #"p"# is pressure in pascals (#"Pa"#)
  • #"V"# is volume in cubic metres ( #"m"^3#)
  • #"n"# is the number of moles
  • #"R"# is the gas constant = #8.314#
  • #"T"# is the temperature in Kelvin (#"K"#)

First, convert your given values into workable units:

  • #1"L" = 0.001"m"^3, :. 2.28"L" = 0.00228"m"^3#
  • #1"atm" = 101325"Pa", :. 1.07"atm" = 108417.8"Pa"#

Second, rearrange the equation to solve for moles:

#"n "=" ""pV"/"RT"#

Next, substitute in your given values and calculate the number of moles:

#"n "=" "(108417.8"Pa" * 0.00228"m"^3)/(8.314 * 279"K")#

#"n "=" "0.1065color(red)(666)255" moles"#

We can then move onto calculating the new pressure value. The first thing to do here is to, again, convert non-compliant units into ones that are accepted by the equation:

  • #1"L" = 0.001"m"^3, :. 1.03"L" = 0.00103"m"^3#

Then we rearrange the equation to solve for pressure:

#"p "=" ""nRT"/"V"#

And substituting in our values, we get:

#"p "=(0.1065666255*8.314 * 307"K")/(0.00103"m"^3)#

#"p "=264078.0989" Pa" = 2.61" atm to 3 significant figures"#