Question

Question #a9717

Answer 1

`1.29 xx 10^7` `"L"`

Explanation:

Any time you're given three of the four primary characteristics of gases (pressure, volume, quantity, and temperature), you'll be using the ideal-gas equation to find the fourth quantity:

`PV = nRT`

When using the ideal-gas equation,

• the pressure `P` must be in atmospheres (`"atm"`)

• the volume `L` must be in liters (`"L"`)

• the quantity `n` must be in moles (`"mol"`)

• the temperature `T` must be the absolute temperature; i.e. in Kelvin (`"K"`)

And `R` is the universal gas constant, `0.08206("L" · "atm")/("mol" · "K")`.

(I'll assume the given quantity `0.600` `"million"` is the number of moles. This is equal to `600,000` `"mol"`)

We need to calculate the Kelvin temperature, which we can do using the equation

`"K" = ""^"o""C" + 273 = 15.0^"o""C" + 273 = color(red)(288` `color(red)("K"`

Now that we have all our necessary variables, we can plug them in to the ideal-gas equation, and rearrange the equation to solve for the volume, `V`:

`V = (nRT)/P = ((600000cancel("mol"))(0.08206("L" · cancel("atm"))/(cancel("mol") · cancel("K")))(288cancel("K")))/(1.10cancel("atm"))`

`= color(blue)(1.29 xx 10^7` `color(blue)("L"`