Respuesta :
Answer: The [tex]CO_{2}[/tex] gas occupies a space of 5.57 L at 26 Celsius and 101.75 kPa.
Explanation:
Given: Mass = 26 g
Pressure = 101.75 kPa
Convert kPa into atm as follows.
[tex]1 kPa = 0.00986923 atm\\101.75 kPa = 101.75 kPa \times \frac{0.00986923 atm}{1 kPa}\\= 1 atm[/tex]
Temperature = [tex]26^{o}C = (26 + 273) K = 299 K[/tex]
Now, moles of a substance is defined as mass of substance divided by its molar mass.
As molar mass of 2,2 dimethyl hexane is 114.23 g/mol. So, its number of moles are calculated as follows.
[tex]No. of moles = \frac{mass}{molar mass}\\= \frac{26}{114.23 g/mol}\\= 0.227 mol[/tex]
Formula used to calculate the volume is as follows.
PV = nRT
where,
P = pressure
V = volume
n = no. of moles
R = gas constant = 0.0821 L atm/mol K
T = temperature
Substitute the values into above formula as follows.
[tex]PV = nRT\\1 atm \times V = 0.227 mol \times 0.0821 L atm/mol K \times 299 K\\V = 5.57 L[/tex]
Thus, we can conclude that the [tex]CO_{2}[/tex] gas occupies a space of 5.57 L at 26 Celsius and 101.75 kPa.
