When a sample of a hydrocarbon fuel is ignited and burned in oxygen, the internal energy decreases by 7.20 kJ. If 5670 J ofheat were transferred to the surroundings, what is the sign and magnitude of work? If the reaction took place in an environ- ment with a pressure of 1 atm, what was the volume change?

Verified step by step guidance

1. First, we need to understand that the internal energy change of a system (ΔU) is given by the equation ΔU = q + w, where q is the heat transferred and w is the work done. In this case, we know that ΔU = -7.20 kJ and q = 5670 J. However, we need to convert q to kJ to match the units of ΔU. So, q = 5670 J * (1 kJ / 1000 J) = 5.67 kJ.
2. Next, we can substitute the values of ΔU and q into the equation to find w. So, -7.20 kJ = 5.67 kJ + w. Solving for w, we get w = -7.20 kJ - 5.67 kJ.
3. Then, we need to understand that the work done by a gas is given by the equation w = -PΔV, where P is the pressure and ΔV is the volume change. In this case, we know that P = 1 atm, but we need to convert it to the same units as w, which is kJ. So, P = 1 atm * (101.3 J / (atm*L)) * (1 kJ / 1000 J) = 0.1013 kJ/L.
4. Now, we can substitute the values of w and P into the equation to find ΔV. So, w = -PΔV becomes w / -P = ΔV.
5. Finally, we can substitute the values of w and P into the equation to find ΔV. So, ΔV = w / -P.

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a chemical reaction, the change in internal energy of the system is equal to the heat added to the system minus the work done by the system. This principle is crucial for understanding how energy is conserved during chemical reactions.

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For a gas, work can be calculated using the formula W = -PΔV, where P is the pressure and ΔV is the change in volume. Understanding how to calculate work is essential for determining the energy changes in a system during a reaction, especially when gases are involved.

Enthalpy and Heat Transfer

Enthalpy is a thermodynamic quantity that represents the total heat content of a system. When a reaction occurs at constant pressure, the heat transferred to or from the surroundings can be related to the change in enthalpy. In this scenario, knowing the heat transferred to the surroundings helps in calculating the work done and understanding the overall energy balance of the reaction.