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0.314 mol of a diatomic molecule has a mass of 22.26g. How would you identify the molecule?

Answer
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Hint :Diatomic molecules are made up of only two atoms, which can be of the same or different chemical elements. The prefix di- comes from Greek and means "two." A diatomic molecule is said to be homonuclear if it contains two atoms of the same element, such as hydrogen or oxygen.

Complete Step By Step Answer:
It is a type of homonuclear diatomic molecule. There are 7 diatomic elements, but only 5 diatomic elements at standard temperature and pressure (STP). The diatomic elements are hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine, and iodine.
To identify the molecule we have one formula,
 $ \text{ }\frac{mass}{molar\text{ }quantity}=\frac{22.26.g}{0.314.mo{{l}^{-1}}}=70.9.g.mo{{l}^{-1}} $ with respect to X2 and thus, the molar mass, with respect to $ X $ was $ 35.45\cdot g\cdot mo{{l}^{-1}} $ , and clearly $ X=Cl $ , i.e. $ {{X}_{2}}\equiv C{{l}_{2}} $ .
As a tip, which I would expect A2 students, and certainly 1st year undergraduates, to know, ALL of the elemental gases (save the Noble Gases), dihydrogen, dinitrogen, dioxygen, dihalogen , are BINUCLEAR, i.e. $ {{H}_{2}},~{{N}_{2}},~{{X}_{2}} $ etc.
And of course $ B{{r}_{2}} $ is a room temperature liquid, and I2 is a room temperature solid.
Thus it is the molar mass of $ Cl $ . Thus the molecule is $ C{{l}_{2}} $ .

Note :
Chlorine is a chemical element with the atomic number 17 and the symbol Cl. It is the second-lightest of the halogens, appearing in the periodic table between fluorine and bromine, and its properties are mostly intermediate between them. At room temperature, chlorine is a yellow-green gas. It is an extremely reactive element and a powerful oxidizing agent: it has the most electrons affinity and the third-highest electronegativity on the Pauling scale, behind only oxygen and fluorine.