Calculating the Temperature of Gas in a Cylinder

Explanation:

To find the temperature of the methane gas in the cylinder, we can use the Ideal Gas Law, which is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin.

First, we must convert the given pressure from mmHg to atm because the gas constant R is typically given in liters·atm/mol·K. 1 atm = 760 mmHg, therefore 3800 mmHg = 3800 mmHg ÷ 760 mmHg/atm = 5 atm.

Next, we calculate the number of moles of methane using its molecular weight (16.04 g/mol):

n = mass of CH4 ÷ molar mass of CH4

n = 4.28 g ÷ 16.04 g/mol = 0.267 moles of CH4

Now, we plug in the values into the Ideal Gas Law and solve for T:

PV = nRT

5 atm × 2.00 L = 0.267 moles × (0.0821 liters·atm/mol·K) × T

T = (5 atm × 2.00 L) ÷ (0.267 moles × 0.0821 liters·atm/mol·K)

T = 367.55 K

Therefore, the temperature of the gas is 367.55 K.