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Biology

What is the correct general equation for cellular respiration?

The general equation for aerobic cellular respiration, the process by which cells convert glucose and oxygen into ATP, is: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP This equation shows that one molecule of glucose (C₆H₁₂O₆) reacts with six molecules of oxygen (O₂) to produce six molecules of carbon dioxide (CO₂), six molecules of water (H₂O), and energy in the form of ATP (adenosine triphosphate). ATP is the primary energy currency of the cell; it stores and transfers energy for nearly all cellular processes. When ATP is broken down into ADP (adenosine diphosphate) and inorganic phosphate (Pi), energy is released to power activities such as muscle contraction, active transport across membranes, protein synthesis, and cell division. Cellular respiration occurs in several stages: glycolysis (in the cytoplasm), the link reaction and Krebs cycle (in the mitochondrial matrix), and the electron transport chain (across the inner mitochondrial membrane). Oxygen is essential in the final stage, acting as the terminal electron acceptor in the electron transport chain, which enables the production of most of the ATP during respiration. In total, aerobic respiration can yield up to 36 to 38 ATP molecules per glucose molecule, making it far more efficient than anaerobic pathways, which produce only 2 ATP per glucose molecule. This efficiency makes aerobic respiration vital for energy-demanding organisms like animals, plants, and many fungi.

Physics

What is the formula to calculate absolute uncertainty?

Most numerical values in science are measurements, and every measurement has an uncertainty. Scientists communicate the uncertainty of their measurements to show their level of confidence in their measurements. If the length of a ramp had been measured to be 80 cm, the absolute uncertainty of the measurement would likely be ± 1 cm. For a time measurement taken by a person with a stopwatch, the absolute uncertainty is normally ± 0.2 s. These are examples of absolute uncertainty. If a series of measurements is being added together or subtracted, the absolute uncertainty of the calculated value is found from the sum of the individual uncertainties on the measurements. For example, consider the addition of the following lengths and their uncertainties. $\hspace{2em}$(2.0 ± 0.1) cm + (8.2 ± 0.2) cm + (2.5 ± 0.5) cm The result will be the sum of the lengths, and the absolute uncertainty will be the sum of the individual uncertainties: $\hspace{2em}$Length = 2.0 + 8.2 + 2.5 = 12.7 cm $\hspace{2em}$Absolute uncertainty = 0.1 + 0.2 + 0.5 = 0.8 cm $\hspace{2em}$The final answer is expressed as 12.7 cm ± 0.8 cm. If two measurements are being multiplied or divided, then the calculation of the absolute uncertainty on the result is more complex. During multiplication or division operations, the relative or fractional uncertainties need to be added together. To do this, the absolute uncertainties on the original measurements must first be converted into fractional uncertainties, and then the fractional uncertainty of the result must be converted back into an absolute uncertainty. Consider the following calculation of the density of an object. The mass m and volume V of the object are measured to be $\hspace{2em}m$ = 4.5 g ± 0.2 g $\hspace{2em}V$ = 2.5 cm$^3$ ± 0.5 cm$^3$ The density can be found from the formula $\hspace{2em}\rho=\dfrac{m}{V}$ Giving $\hspace{2em}\rho=\dfrac{4.5\ \ce{g}}{2.5\ \ce{cm}^{3} }=1.8 $ g cm$^{-3}$ Now we need to find the absolute uncertainty on the result. First we find the fractional uncertainties on the mass and the volume: $\hspace{2em}$ $\dfrac{\Delta{m}}{m}=\dfrac{0.2}{4.5} \hspace{3em} \ce{and} \hspace{3em} \dfrac{\Delta V}{V} =\dfrac{0.5}{2.5}$ Because we are dividing the terms, we add the fractional uncertainties $\hspace{2em}$ $\dfrac{\Delta{m}}{m} + \dfrac{\Delta V}{V} = \dfrac{0.2}{4.5} + \dfrac{0.5}{2.5} = 0.24$ Knowing that $\hspace{2em}$ $\dfrac{\Delta \rho}{\rho}=0.24$ (this can also be expressed as 24%) We can now solve for ∆p: $\hspace{2em}$ $\Delta \rho = (0.24)\rho =(0.24)(1.8)=0.4\ \ce{g cm}^{-3}$ Our final value for density, with its absolute uncertainty, becomes $\hspace{2em}$ $\rho =1.8\ \ce{g cm}^{-3} ± 0.4\ \ce{g cm}^{-3}$

History

How did mercantilism increase the likelihood of conflicts between European powers?

Mercantilism was an economic system that was prevalent from the 16th through the 18th centuries, in which governments intervened heavily in their country’s economic activities to protect and promote their own national interests by applying tariffs, quotas, and other restrictions with a goal of maintaining a favorable balance of trade (greater exports than imports). Good examples of this system include England/Great Britain, France, Spain, Portugal, and the Netherlands (Dutch Republic). One element of this system was to drive the creation of colonies, which were forced to provide raw materials to the controlling colonial power. These colonial territories were often simultaneously forced to purchase finished manufactured goods from the colonizing nation, thus further exaggerating the balance of trade between the two. European powers were the primary colonizers during this period, and their maintenance of power relied on the economic benefits of mercantilism. As a result, this often drew them into conflicts over particularly valuable colonial territories, for both the raw materials and purchasing markets they could provide. Furthermore, because these powers viewed the world’s wealth and resources as a zero-sum scenario, control of these resources drove trade wars, military buildup (especially powerful navies), and in many cases, outright war, such as the Anglo-Dutch Wars and the Seven Years’ War.

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