Explanation
Molar mass $$NH_3$$ = 14+3 = 17g/mol
Given mass = 4.25g
No of moles= $$\dfrac{given\ mass}{molar\ mass}$$
No of moles = 4.25/17 = 0.25 mol of $$NH_3$$
1 mol of $$NH_3$$ contains $$6.022\times 10^{23}$$ molecules
0.25 mol $$NH_3$$ contains $$0.25 \times$$$$6.022\times 10^{23}$$ = $$1.5055\times$$ $$10^{23}$$ molecules
Number of moles = $$\dfrac {Mass} {Molar mass}$$
Number of atoms = $$Moles\times6.023\times10^{23}$$
Step 1: The mass of iron in $$50$$ gram.
Here, $$50$$ gram already denotes the mass of iron.
Step 2: The mass of $$5$$ moles of nitrogen gas
According to moles formula mentioned above,
The mass of nitrogen = $$5\times 28=140g$$
Step 3: The mass of $$1$$ gm atoms.
$$1$$ gm atoms= $$1$$ mole of any atom
Step 4: The mass of $$5\times10^{23}$$ atoms of carbon.
Using above formula,
Mass of carbon = $$\dfrac {12\times5\times10^{23}} {6.023\times10^{23}} = 9.96gm$$
Among all , $$5$$ moles of nitrogen has highest mass of $$140g$$
Final answer:
Option $$B$$ is correct answer
Given,
Number of molecules of $$X = 3\times 10^{21}$$
Number of molecules of $$Y = 4.5\times 10^{25}$$
Molecular weight of $$X = 50$$
Total mass of mixture $$= 1\ g$$
Formula used :
$$Mass\ of\ mixture=\left[\dfrac{Number\ of\ molecules\ of\ X}{Avogrado's\ Number} \times Molar\ Mass\ of\ X\right]$$
$$+\left[\dfrac{Number\ of\ molecules\ of\ Y}{Avogrado's\ Number}\times Molar\ Mass\ of\ Y\right]$$
Now, putting all the given values in this formula, we get the molecular mass of $$Y$$.
$$1=\left[\dfrac{3\times 10^{21}}{6.023\times 10^{23}}\times 50\right]+\left[\dfrac{4.5\times 10^{25}}{6.023\times 10^{23}}\times Y\right]$$
$$\Rightarrow 1=\dfrac{150\times 10^{21}+4.5Y\times 10^{25}}{6.023\times 10^{23}}$$
$$\Rightarrow 6.023\times 10^{23}=10^{21}(150+4.5Y\times 10^4)$$
$$\Rightarrow \dfrac{6.023\times 10^{23}}{10^{21}}=150+4500Y$$
$$\Rightarrow 602.3=150+4500Y$$
$$\Rightarrow 4500Y=602.3-150$$
$$\Rightarrow Y = \dfrac{450.3}{4500}$$
$$Y= 150$$
Therefore, on solving, we get $$Y=150$$
Therefore, the molecular weight of $$Y$$ is $$150g$$.
Hence option (B) is correct.
Hint: The minimum number of Sulphur atoms which a molecule can possess is one.
Step 1: Finding the molecular mass of the compound.
$$Mass\ of\ 1\ sulphur\ atom\ =\ 32 \ grams.$$
$$ As\ the\ compound\ has\ 8\% \ sulphur\ by\ mass,$$
$$\therefore 8 \ grams\ of\ sulphur\ is\ present\ in\ 100 \ grams\ of\ compound.$$
$$\therefore 32 \ grams\ of\ sulphur\ is\ present\ in\ \dfrac{32}{8} \times 100=400\ grams \ of\ compound.$$
$$Hence,\ the\ least\ molecular\ mass\ of\ the\ compound\ is\ 400 \ grams.$$
Final Step: Correct answer - (C) The least molecular mass of the compound is $$400 \ grams.$$
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