Question

The volume of gas in the discharge tube is $1.12\times {{10}^{-7}}$ mL at STP. Then the number of molecules of gas in the tube is?
(a)- $3.01 \times { 10 }^{ 4 }$
(b)- $3.01 \times { 10 }^{ 15 }$
(c)- $3.01 \times { 10 }^{ 12 }$
(d)- $3.01 \times { 10 }^{ 16 }$

Answer 1

Hint: To solve this, firstly find out the number of moles in mL of the gas in the discharge tube. Then, multiply it by Avogadro's number to find out the required answer.

Complete answer:
We know that, STP in chemistry is the abbreviation for Standard Temperature and Pressure. STP most commonly is used when performing calculations on gases, such as gas density. The standard temperature is 273 K and the standard pressure is 1 atm pressure. This is the freezing point pure water at sea level atmospheric pressure. At STP, one mole of gas occupies 22.4L of molar volume.
Now, first let us know a few terms which we will be using to solve the given question.
Molar Volume: The molar volume is nothing but the volume of 1 mole of substance. It can be simply found by dividing the volume of a sample by the number of moles of that particular sample. $V_m$ = $V_n$ this is simply the inverse of the number density.
Molar Volume Formula:
The Molar volume is directly proportional to molar mass and inversely proportional to density. The formula of the molar volume is expressed as
${{V}_{m}} = \dfrac{Molar\text{ }mass}{Density}$
Now, let us try to solve it!
In 22400 m L there is 1 mol present,
So, number of moles in $1.12 \times {{10}^{-7}}$ , will have moles as follows,
Number of moles =$ \dfrac { 1.12 \times { 10 }^{ -7 } }{ 22400 }$
As we know Avogadro’s number, ${{N}_{A}} = 6.022 \times {{10}^{23}}$
So, the number of molecules = $\dfrac { 1.12 \times { 10 }^{ -7 } }{ 22400 } \times { N }_{ A } = 3.01 \times { 10 }^{ 12 }$

Therefore, the correct answer is option [C] $3.01 \times { 10 }^{ 12 }$

Note:
We should not be confused between NTP and STP. NTP is normal temperature and pressure whereas STP is standard temperature and pressure. STP is set by IUPAC which is the International Union of Pure and Applied Chemistry as ${{0}^{{}^\circ }}$ Celsius and 100 kPa or 1 bar. NTP is set as 101.325 kPa and ${{20}^{{}^\circ }}$ Celsius temperature.