Ideal Gas Equation

We will use the ideal gas equation to solve this problem: $PV%20%3D%20nRT$ Where:
- $P$ is the pressure (in pascals),
- $V$ is the volume (in cubic meters),
- $n$ is the number of moles,
- $R$ is the universal gas constant $8.31%20%5C%2C%20%5Ctext%7BJ%20mol%7D%5E%7B-1%7D%20%5C%2C%20%5Ctext%7BK%7D%5E%7B-1%7D$ , - $T$ is the temperature (in kelvins).
Given: - Volume $V%20%3D%20300%20%5C%2C%20%5Ctext%7Bcm%7D%5E3%20%3D%20300%20%5Ctimes%2010%5E%7B-6%7D%20%5C%2C%20%5Ctext%7Bm%7D%5E3$ ,
- Pressure $P%20%3D%201%20%5C%2C%20%5Ctext%7Bmm%20of%20mercury%7D%20%3D%201%20%5Ctimes%20133.322%20%5C%2C%20%5Ctext%7BPa%7D$ ,
- Temperature $T%20%3D%2027%C2%B0C%20%3D%20300%20%5C%2C%20%5Ctext%7BK%7D$ .
Using the ideal gas equation, we can find the number of moles $n$ : $n%20%3D%20%5Cfrac%7BPV%7D%7BRT%7D$ Substituting the known values: $n%20%3D%20%5Cfrac%7B(1%20%5Ctimes%20133.322)%20%5Ctimes%20(300%20%5Ctimes%2010%5E%7B-6%7D)%7D%7B(8.31)%20%5Ctimes%20(300)%7D$ $n%20%3D%205.36%20%5Ctimes%2010%5E%7B-5%7D%20%5C%2C%20%5Ctext%7Bmoles%7D$ Now, the number of molecules is: $N%20%3D%20n%20%5Ctimes%20N_A$ Substituting the known value for $N_A$ : $N%20%3D%20(5.36%20%5Ctimes%2010%5E%7B-5%7D)%20%5Ctimes%20(6.02%20%5Ctimes%2010%5E%7B23%7D)$ $N%20%3D%203.23%20%5Ctimes%2010%5E%7B19%7D$ Therefore, the number of molecules is approximately $9.65%20%5Ctimes%2010%5E%7B18%7D$ as given in option D.

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

Official Solution

Ideal Gas Equation

High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Chapter Questions
3 MCQs