Question

Mass of 112 mL of a certain gas is 0.22 g at STP. How many molecules are there in the
sample of gas ? What is the molar mass of the gas ?​

Answer 1

Answer :-

→ Number of molecules are 3.011 × 10²¹ .

→ Molar mass of the gas is 44 g/mol .

Explanation :-

We have :-

• Volume of the gas = 112 mL = 0.112 L

• Mass = 0.22 g

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At STP condition :-

• Pressure (P) = 1 atm

• Temperature (T) = 273 K

Firstly, let's calculate the number of moles of the gas using Ideal Gas equation :-

PV = nRT

⇒ 1 × 0.112 = n × 0.0821 × 273

⇒ 0.112 = 22.4n

⇒ n = 0.112/22.4

⇒ n = 0.005

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Number of molecules :-

= No of moles × Avogadro Number

= 0.005 × 6.022 × 10²³

= 0.03011 × 10²³

= 3.011 × 10²¹ molecules

Molar mass :-

= Given Mass/No of moles

= 0.22/0.005

= 220/5

= 44 g/mol

Answer 2

$\red{\bigstar}$ G I V E N

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◈ Mass of 112 ml of a certain gas is 0.22 g at STP

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$\blue{\bigstar}$ T OㅤF I N D

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◈ How many molecules are there in the sample of gas?

◈ What is the molar mass of the gas?

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$\purple{\bigstar}$ S O L U T I O N

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Converting units of volume from ml to l ::

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$\sf \quad \dashrightarrow \quad 1\:ml = 1000\:l$

$\\ \sf \quad \dashrightarrow \quad 112\:ml = \dfrac{112}{1000}\:l$

$\\ \sf \quad \dashrightarrow \quad \purple{112\:ml = 0.112\:l}$

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Finding number of moles ::

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$\underline{\sf{\bigstar\:As\:we\:know\:that\:::}}$

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$\underline{\boxed{\sf{Number\:of\:moles = \dfrac{Volume}{Volume\:at\:STP}}}}$

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Putting all known values ::

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$\sf \quad \dashrightarrow\quad Number\:of\:moles = \dfrac{0.112}{22.4}$

$\\ \quad \sf \dashrightarrow\quad\green{Number\:of\:moles = 0.005\:mol}$

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Finding number of molecules ::

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$\underline{\boxed{\sf{1\:mol = 6.022\:\times\:10^{23}\:molecules }}}$

$\\ \small \sf \dashrightarrow\: 0.005\:mol = 0.005\:\times\:6.022\:\times\:10^{23}\:molecules$

$\\ \small \sf \dashrightarrow\: 0.005\:mol = 0.03011\:\times\:10^{23}\:molecules$

$\\ \small \sf \dashrightarrow\:\orange{ Number\:of\:molecules = 3.011\:\times\:10^{21}}$

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Finding molar mass ::

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$\underline{\sf{\bigstar\:As\:we\:know\:that\:::}}$

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$\underline{\boxed{\sf{Number\:of\:moles = \dfrac{Given\:Mass}{Molar\:Mass}}}}$

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Putting all known values ::

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$\sf \quad\dashrightarrow\quad 0.005 = \dfrac{0.22}{Molar\:Mass}$

$\\ \sf \quad\dashrightarrow\quad Molar\:Mass = \dfrac{0.22}{0.005}$

$\\ \sf \quad\dashrightarrow\quad \pink{Molar\:Mass = 44\:g}$

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$\red{\bigstar}$ H E N C E

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»» Number of molecules = 3.011 × 10²¹

»» Molar Mass = 44 g

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