Total Kinetic energy = n(3/2 RT0)
Where, n = Number of moles of the gas
R = Gas constant
T = Absolute Temperature
Molecular weight of Methane ,
CH4 = 12 + 4 *1 = 16
Therefore, number of moles of methane in 8g of methane,
= 8.0/16.0 =0.5
R = 8.314 joules/K/mole
T = 27+273 = 300K
Therefore ,Total kinetic of the molecules in 8g of methane at 300 K is
= Inl *3/2 RT
= 0.5*3/2*8.314*300
= 1870.65 joules
Avg. Kinetic energy = 1870.65/6.023*10^23 *0.5= 6.21 *10^-21 joules/molecules

Introduction:
In order to calculate the total kinetic energy of the molecules in 8g of methane at 27 degrees Celsius, we need to consider the formula for kinetic energy and the properties of methane.

Formula for kinetic energy:
The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass, and v is the velocity of the particles.

Properties of methane:
Methane (CH4) is a simple hydrocarbon gas. Its molar mass is approximately 16.04 g/mol. We can use this information to calculate the number of moles present in 8g of methane.

Calculating the number of moles:
To calculate the number of moles, we can use the formula:
moles = mass / molar mass

Given that the mass of methane is 8g and the molar mass is 16.04 g/mol, we can substitute these values into the formula:
moles = 8g / 16.04 g/mol = 0.498 mol

Calculating the velocity:
To calculate the velocity, we can use the formula:
v = sqrt(3 * RT / m)
where R is the ideal gas constant and T is the temperature in Kelvin.

Given that the temperature is 27 degrees Celsius, we need to convert it to Kelvin:
T(K) = T(C) + 273.15 = 27 + 273.15 = 300.15 K

Using the value of the ideal gas constant R = 8.314 J/(mol·K) and the molar mass of methane m = 16.04 g/mol, we can substitute these values into the formula:
v = sqrt(3 * 8.314 J/(mol·K) * 300.15 K / 16.04 g/mol) = 1561.7 m/s

Calculating the kinetic energy:
Now that we have the mass and velocity, we can substitute these values into the formula for kinetic energy:
KE = 1/2 * m * v^2
KE = 1/2 * 0.498 mol * (1561.7 m/s)^2

Calculating the kinetic energy gives us the answer in joules.

Conclusion:
The total kinetic energy of the molecules in 8g of methane at 27 degrees Celsius is calculated using the formula for kinetic energy, considering the properties of methane. The final result will depend on the specific calculations performed.