Question

How many molecules are in 7.62 L of CH4, at 87.5°C and 722 torr

Answer 1

Answer: There are
`1.469 * 10^(23)` molecules present in 7.62 L of
`CH_4` at
`87.5^(o)C` and 722 torr.

Step-by-step explanation:

Given : Volume = 7.62 L

Temperature =
`87.5^(o)C = (87.5 + 273) K = 360.5 K`

Pressure = 722 torr

1 torr = 0.00131579

Converting torr into atm as follows.

`722 torr = 722 torr * (0.00131579 atm)/(1 torr)\\= 0.95 atm`

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.

`PV = nRT\\0.95 atm * 7.62 L = n * 0.0821 L atm/mol K * 360.5 K\\n = (0.95 atm * 7.62 L)/(0.0821 L atm/mol K * 360.5 K)\\= (7.239)/(29.59705)\\= 0.244 mol`

According to the mole concept, 1 mole of every substance contains
`6.022 * 10^(23)` atoms. Hence, number of atoms or molecules present in 0.244 mol are calculated as follows.

`0.244 mol * 6.022 * 10^(23)\\= 1.469 * 10^(23)`

Thus, we can conclude that there are
`1.469 * 10^(23)` molecules present in 7.62 L of
`CH_4` at
`87.5^(o)C` and 722 torr.