How much work,in joules,is done when the pressure is suddenly released from 4.56 atm to 1.23 atm on 45.4 g of O₂ at 44 °C? A)386 ^J B)-477 ^J C)-2.74 × 10^{3 J} D)2.74 × 10^{3 J} E)477 ^J

Question

Quizplus · Accepted Answer

The work done is given by the formula: W = -PΔV Where P is the initial pressure, ΔV is the change in volume, and the negative sign indicates that the work done is against the surroundings. To find ΔV, we can use the ideal gas law: PV = nRT Where n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. Rearranging, we get: V = (nRT)/P We can calculate the initial volume and the final volume using this equation and then find the difference. However, since the number of moles (n) is not given, we cannot do this directly. Instead, we can use the fact that the mass of the gas is given and assume that it represents one mole of gas. The molar mass of O₂ is 32 g/mol. Therefore, 45.4 g of O₂ is equal to 1.42 moles. Using the ideal gas law, we can find the initial volume: V1 = (nRT)/P1 = (1.42 mol)(0.0821 L·atm/mol·K)(44+273 K)/(4.56 atm) = 14.6 L Similarly, we can find the final volume: V2 = (nRT)/P2 = (1.42 mol)(0.0821 L·atm/mol·K)(44+273 K)/(1.23 atm) = 52.2 L Therefore, ΔV = V2 - V1 = 37.6 L Now we can calculate the work done: W = -PΔV = -(4.56 atm)(37.6 L - 14.6 L) = -103.8 L·atm To convert L·atm to joules, we can use the conversion factor 1 L·atm = 101.3 J: W = (-103.8 L·atm)(101.3 J/L·atm) = -10518.5 J Therefore, the work done is -10518.5 J, which corresponds to answer choice C.

How Much Work,in Joules,is Done When the Pressure Is Suddenly