Why does our heart rate increase when we run compared to when we are sitting?

Running demands a lot of energy in our leg muscles in order for them to contract and relax. Energy is released in the process of respiration which breaks down glucose into ATP. The equation for respiration is as follows: glucose + oxygen -> carbon dioxide + water
Blood carries all the reactants required (glucose and oxygen) and also the by-products (carbon dioxide and water) of respiration. When there is a high demand for respiration, such as during physical activity, there is a higher demand for oxygen and glucose in our muscles therefore our heart pumps faster to meet the demand. With increased respiration there is also a build-up of by-products (mainly carbon dioxide) that need to be removed. Increased heart rate will quickly transport the carbon dioxide to the lungs where it can be exhaled.