Final answer:
The volume of 4.00 moles of methane gas at 15°C and 1.60 atm is calculated using the Ideal Gas Law formula PV = nRT. After converting the temperature to Kelvin and using the ideal gas constant 0.0821 L·atm/(mol·K), the volume is found to be approximately 58.63 liters.
Step-by-step explanation:
To calculate the volume of 4.00 moles of methane gas (CH₄) at 15℃ and 1.60 atm, 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 ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature to Kelvin:
- T(K) = T(℃) + 273.15 = 15 + 273.15 = 288.15 K
Next, we use the ideal gas constant in L·atm/(mol·K), which is 0.0821.
By substituting our given values into the Ideal Gas Law and solving for volume V:
- V = (nRT)/P
- V = (4.00 mol × 0.0821 L·atm/(mol·K) × 288.15 K) / 1.60 atm
- V = (4.00 × 0.0821 × 288.15) / 1.60
- V ≈ 58.63 liters
The volume of 4.00 moles of methane gas at 15℃ and 1.60 atm is approximately 58.63 liters.