Question

Calculate the number of molecules in a sample of
an ideal gas whose volume is 0.45 L at 67°C and
0.76 bar pressure.​

Answer 1

Answer:

$\bigstar{\bold{Number\:of\:molecules = 7.2 \times 10^{21} molecules}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Pressure (P) = 0.76 bar
• Volume (V) = 0.45 L
• Temperature (T) = 67° C

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Number of molecules of the gas

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First convert the temperature from °C to K

  67° C = 67 + 273.15 = 340.15 K

→ Now convert the pressure from bar to atm

  0.76 bar = 0.75 atm

→ Now we have to find the number of moles of gas

→ By ideal gas equation we know that,

  PV =  n R T

  where R is the gas constant and the value of R = 0.0821 L atm mol⁻¹ K⁻¹

→ Substitute the given datas

   0.75 atm × 0.45 L = n × 0.0821 L atm mol⁻¹ K⁻¹ × 340.15 K

   n = (0.3375/27.926) mol

   n = 0.012 mol

→ Hence the number of moles of gas is 0.012 moles.

→ Now the number of molecules of gas is given by

  Number of molecules of gas = number of moles × Avogadro's number

  where Avogadro's number = 6.022 × 10²³

→ Substituting the values,

  Number of molecules = 0.012 × 6.022 × 10 ²³

  Number of molecules = 0.072 × 10²³

  Number of molecules = 7.2 × 10²¹ molecules

$\boxed{\bold{Number\:of\:molecules = 7.2 \times 10^{21} molecules}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The ideal gas equation is given by

   PV = n R T

   where P is the pressure, V = volume, n = number of moles, R = gas constant, T = temperature