Final answer:
To find the volume occupied by 19.6 g of methane at 27°C and 1.59 atm, calculate the number of moles of methane, convert the temperature to Kelvin, then apply the Ideal Gas Law to find the volume.
Step-by-step explanation:
The volume occupied by 19.6 g of methane, CH4, at 27°C and 1.59 atm can be calculated using the Ideal Gas Law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. First, convert the mass of methane to moles by using the molar mass of methane (16.04 g/mol). Then convert the temperature to Kelvin (300 K). With the values for n, P, T, and R (0.0821 L·atm/K·mol), we can solve for V, the volume.
Calculate moles of methane: n = 19.6 g × (1 mol / 16.04 g) = 1.22 mol
Convert temperature to Kelvin: T = 27 + 273 = 300 K
Use Ideal Gas Law to find volume: V = (nRT) / P = (1.22 mol × 0.0821 L·atm/K·mol × 300 K) / 1.59 atm
Perform the calculation to find the volume V.