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Question: How many molecules are present in one gram of hydrogen? A. \(6.02\times {{10}^{23}}\) B. \(3.02\...

How many molecules are present in one gram of hydrogen?
A. 6.02×10236.02\times {{10}^{23}}
B. 3.02×10233.02\times {{10}^{23}}
C. 2.5×10232.5\times {{10}^{23}}
D. 1.5×10231.5\times {{10}^{23}}

Explanation

Solution

Try to find out the number of moles of Hydrogen by using the molar mass and given weight. Hydrogen exists as a diatomic molecule. With the number of moles, calculate the number of molecules present.

Complete step by step answer:
In order to answer our question, we need to have an idea about the moles, molar mass and Avogadro’s number. For example, an element is given and its weight is known to us. Now, each element consists of atoms, but we do not know how many particles or atoms are inside that particular element or compound. So, here we use the concept of Avogadro’s number. The value of Avogadro’s number is 6.022×10236.022\times {{10}^{23}}. So the mass of the element which contains exactly the number of atoms as the Avogadro’s constant is said to be 1 mole. And this mass, which contains the Avogadro number of atoms in it is called the molar mass. For example, an Oxygen molecule has the molar mass of 32g mol−132g\,mo{{l}^{-1}}. That means that when 32 grams of oxygen is taken, then there are exactly 6.022×10236.022\times {{10}^{23}}atoms in it. And this corresponds to 1 mole of the oxygen molecule. Now, the number of moles is determined mathematically by:
no of mole=given massmolar massno\,of\,mole=\dfrac{given\,mass}{molar\,mass}

Now, let us come back to our question. We have been given the hydrogen atom. Hydrogen is the first element in the periodic table and has a molar mass of 1g mol−11g\,mo{{l}^{-1}}. However, hydrogen exist in the molecular diatomic state as H2{{H}_{2}}, so its molar mass will be 2×1 g mol−1=2 g mol−12\times 1\,g\,mo{{l}^{-1}}=2\,g\,mo{{l}^{-1}}. So, we have our given mass=1g1g and the molar mass as 2g mol−12g\,mo{{l}^{-1}}. So, using the formula, we can calculate the number of moles of hydrogen which is:
moleH2=1g2g mol−1=0.5mol{{e}_{{{H}_{2}}}}=\dfrac{1g}{2g\,mo{{l}^{-1}}}=0.5

Now, 1 mole corresponds to 6.022×10236.022\times {{10}^{23}} molecules.
So, 0.5 mole corresponds to half of it, which is 3.02×10233.02\times {{10}^{23}} molecules.
So, the correct answer is “Option B”.

Note: The number of moles is a dimensional quantity. Although it may be seen that molar mass has a unit of mass i.e gram, it is not. The unit of molar mass is in gram mol−1gram\,mo{{l}^{-1}}, unless one mole of the substance is given.