Answer: There are [tex]1.469 \times 10^{23}[/tex] molecules present in 7.62 L of [tex]CH_4[/tex] at [tex]87.5^{o}C[/tex] and 722 torr.
Explanation:
Given : Volume = 7.62 L
Temperature = [tex]87.5^{o}C = (87.5 + 273) K = 360.5 K[/tex]
Pressure = 722 torr
1 torr = 0.00131579
Converting torr into atm as follows.
[tex]722 torr = 722 torr \times \frac{0.00131579 atm}{1 torr}\\= 0.95 atm[/tex]
Therefore, using the ideal gas equation the number of moles are calculated as follows.
PV = nRT
where,
P = pressure
V = volume
n = number of moles
R = gas constant = 0.0821 L atm/mol K
T = temperature
Substitute the values into above formula as follows.
[tex]PV = nRT\\0.95 atm \times 7.62 L = n \times 0.0821 L atm/mol K \times 360.5 K\\n = \frac{0.95 atm \times 7.62 L}{0.0821 L atm/mol K \times 360.5 K}\\= \frac{7.239}{29.59705}\\= 0.244 mol[/tex]
According to the mole concept, 1 mole of every substance contains [tex]6.022 \times 10^{23}[/tex] atoms. Hence, number of atoms or molecules present in 0.244 mol are calculated as follows.
[tex]0.244 mol \times 6.022 \times 10^{23}\\= 1.469 \times 10^{23}[/tex]
Thus, we can conclude that there are [tex]1.469 \times 10^{23}[/tex] molecules present in 7.62 L of [tex]CH_4[/tex] at [tex]87.5^{o}C[/tex] and 722 torr.
