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It is false that in an energy diagram for a chemical reaction, energy is plotted along the x-axis (the horizontal axis) and reaction progress is plotted along the y-axis (the vertical axis). The energy is actually plotted along the y-axis and the reaction along the x-axis.
In the diagram on the right, the energy is taken from the surroundings and stored as potential energy in the products. (a) is the activation energy for the reaction to take place whilst (c) is the energy change (known as enthalpy change).