Question

A quantity of a gas at a temperature of `223` `K` has a volume of `100.0` `dm^3` To what temperature must the gas be raised, while the pressure is kept constant, to give a volume of `185` `dm^3`?

Answer 1

`"412.6 K"`

Explanation:

`"Let us recall the gas law"`

`"PV = nRT"`

Our question is that a quantity of a gas at a temperature of
223K has a volume of `"100.0 dm"^3`.

To what temperature must the gas be raised, while the pressure is kept constant, to give a volume of `"185 dm"^3` ?

So let;s rearrange the formula

`P = "(nRT)"/V`

`Where V = 100.0dm^3`

`"Where p = is unknown or x"`

`"Where R = gas constant law which is 0.0821L"`

`"Where n = n is number of moles of gas"`

So let us plug in the variables

`"100 dm"^3` should be converted in litres first.

`"1 dm"^3 = "1 L"`

So

`"100 dm"^3 = "100 L"`

`(n * 0.0821L * 223K) /(100L) = "18.309n"/"100L" = 0.18309n`

So if pressure is constant to get a 185dm^3

The expression would be

`185dm^3 = (n * 0.0821L * T)/(0.18309n)`

Cut out the both n

`185dm^3 = 0.0821 * T/"0.18309"`

`"so T = Let's solve your equation step-by-step."`

`185="0.0821t"/0.18309`

Step 1: Multiply both sides by 0.18309.

`185="0.0821t"/0.18309`

`(185) * (0.18309) = ("0.0821t" * 0.18309) * (0.18309) = 33.87165=0.0821t`

Step 2: Flip the equation.

`0.0821t=33.87165`

Step 3: Divide both sides by 0.0821.

`"0.0821t"/0.0821 = 33.87165/0.0821`

`t=412.565773`

Answer:

`T= "412.6 K"`