Question

How can I calculate the volume , in liters, of $1.50mol$ $C{l_2}$ at STP?

Answer 1

We have to know that for calculating volume of gas molecules, we are actually using ideal gas law which is as $PV = nRT$. It is an equation which defines the states of hypothetical gases that are expressed mathematically by a combination of empirical and physical constants.

We have to remember here that the quantities of pressure, temperature are not provided in the given question but it is giving us a clue that it is at STP which will enable us to know indirectly the actual temperature and pressure. Actually to proceed with this, we have to know that STP is the one which is signifying standard temperature and also standard pressure.

Formula used: $PV = nRT$
Where , $P =$ pressure of gas
$V =$ volume of the gas
$n =$ amount of substance or number of moles in a gas
$R =$ universal gas constant
$T =$ absolute temperature of gas

Complete step-by-step answer:
First of all we have to know that the volume occupied by one mole of a chemical compound or chemical element at STP condition or standard temperature and pressure condition , is actually termed as molar volume since the given questions states to find the volume at STP.

So, before proceeding to the calculation we must note down the quantities to be put on the ideal gas law equation. Before that we have to know the pressure and temperature which is not directly given in the question whereas the other quantities are known.

Since it is given that the volume is to be find in STP condition, we should know that at STP , pressure and temperature is as follows,
$P = 1atm$
$T = 273K$

Now, let us write down the given and known quantities regarding the question.
$\Rightarrow n = 1.50mol$ (given in question)
$\Rightarrow R = 0.0821\dfrac{{atmL}}{{molK}}$ (universal gas constant)
Now , let us write down the ideal gas law equation which is as follows, $PV = nRT$

Before directly putting down values in the above equation for finding volume, let us modify the equation first so as to keep the remaining volume in the left hand side for an easy calculation. The modified equation is as follows,
$\Rightarrow V = \dfrac{{nRT}}{P}$
Next, let us substitute the values in the above modified equation.
$\Rightarrow V = \dfrac{{(1.50mol)(0.0821\dfrac{{atmL}}{{molK}})(273K)}}{{1 atm}}$
$\Rightarrow V = 33.6L/mol$
In this way ,we calculate the volume in liters which is equal to $33.6L$ , of $1.50mol$ $C{l_2}$ at STP.

Note: First of all we should be familiar with the ideal gas law equation as then only we can recognize the equation at first glance when the question is given and proceed to further calculation. The main point we have to keep in mind is if we know the equation also, we cannot move to calculation as some of the quantities are not directly given by the question.

In this condition, we have to know that the only clue to move further is about STP. So, we should know that STP condition signifies the standard temperature at zero degree Celsius as well as standard pressure at one atmospheric pressure. Scientists actually use standards like STP definitions for determining quantitative metrics and also to allow repeatable and consistent experiments. We have to remember always that the same steps can be followed for finding the volume of any gas molecules which are at STP condition.