Question

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?

Answer 1

`"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"`