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Question: When 1 L of \(C{{O}_{2}}\) is heated with graphite, the volume of the gases collected is 1.5 L Calcu...

When 1 L of CO2C{{O}_{2}} is heated with graphite, the volume of the gases collected is 1.5 L Calculate the number of moles of CO produced at STP.
A.111.2\dfrac{1}{11.2}

B.2822.4\dfrac{28}{22.4}

C.122.4\dfrac{1}{22.4}

D.1122.4\dfrac{11}{22.4}

Explanation

Solution

The reaction has to be written and then the changes in volume before and after the reaction need to be observed. From there we can find the amount of CO used, and then using a unitary method, we can find out the moles, using STP condition.

Complete Solution :
- In order to answer our question, we need to learn about mole concept, as well as STP and NTP. Let us talk about moles first. Now, every element, compound as well as an atom possesses some weight. It is expected that more the number of particles, more will be the weight. However, the weight of these minutely small atoms are very small and a better and conventional method is needed to decode them. Now, the number 6.022×10236.022\times {{10}^{23}} is a very special number and is referred to as the Avogadro’s constant. All the particles which constitute an atom / element / molecule which have the Avogadro’s constant of particles have a specific weight. This weight is called the molar mass of the element or compound. For example, carbon has the molar mass of 12 grams. It indirectly means that when 6.022×10236.022\times {{10}^{23}} carbon atoms are taken, then the weight of all those particles is 12 grams. Every different substance has different molar masses.
- The meaning of STP is standard temperature and pressure and it is a collection for constants taken in standard conditions. In STP condition, the pressure is standardised as 1 bar and the temperature is standardised as 273K. Now, let us come to the question and observe the reaction, along with volume consumed:
CO2(g)  +  C(s)→2CO(g)     1L             0L               0L (1−x)L                           2xL \begin{aligned} & C{{O}_{2}}(g)\,\,+\,\,C(s)\to 2CO(g) \\\ & \,\,\,\,1L\,\,\,\,\,\,\,\,\,\,\,\,\,0L\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0L \\\ & (1-x)L\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2xL \\\ \end{aligned}
Here, ‘x’ is the required amount. The total volume comes out to be (1−x)+2x=(x+1) L(1-x)+2x=(x+1)\,L But, it is given that the total volume is 1.5 L. So, on equating, we have:

& x + 1 = 1.5 \\\ & \Rightarrow x = 0.5 \\\ \end{aligned}$$ Amount of CO consumed is 1 litre, and in STP conditions, 22.4 litres of CO should be given by 1 litre of CO. The amount of CO is 1 litre, so the number of moles should be $\dfrac{1}{22.4}$, by using a unitary method. **So, the correct answer is “Option C”.** **Note:** It is to be noted that the principle of STP is based on the ideal gas equation i.e $PV=nRT$. Here, n and R is constant, however in the STP condition, P and T also become constant which gives us the volume as 22.4 litres, and it is true for any gas.