If -9/5 < -3t + 1 < -7/4, what is one possible value of 9t-3?
The quickest way to solve this problem is attained by recognizing that 9t-3 = (-3t + 1) * -3 and multiplying the inequality by -3 accordingly. This gives us the range of possible values for 9t - 3: -9/5 < -3t + 1 < -7/4 27/5 > 9t - 3 > 21/4 The longer way to solve this problem involves first finding solving the inequality for t and then plugging this into 9t-3: -9/5 < -3t + 1 < -7/4 -14/5 < -3t < -11/4 14/15 > t > 11/12 126/15 > 9t > 99/12 --> 42/5 > 9t > 33/4 27/5 > 9t - 3 > 21/4
How can Le Chatelier's principle be applied to explain the effects of adding heat to a reversible endothermic reaction, such as N2O4(g) <---> 2 NO2(g)?
Le Chatelier's principle, which states that if a stress is applied to a system, the system shifts to relieve that applied stress, can be used to determine which way (forward or reverse) the position of equilibrium will move given certain changes in reactant/product concentration, pressure/volume, and/or temperature. While changing the temperature of a reaction does not affect the reaction quotient Qc or Qp, it does change Keq, and the system must then move in whichever direction allows it to reach a new equilibrium state at the new temperature. This direction is determined by the enthalpy of the reaction; intuitively, if the reaction is endothermic (absorbs energy/heat from its surroundings), heat functions as a reactant, and if the reaction is exothermic (releases energy/heat to its surroundings), heat acts as a product. In the case of the endothermic reaction N2O4(g) <---> 2 NO2(g), applying these principles gives N2O4(g) + heat <---> 2 NO2(g), and by increasing the temperature of the reaction, we increase the heat, which functions as a reactant. Like all equilibrium problems, increasing the value of a reactant results in the forward movement of the equilibrium position (towards the products), thereby increasing the concentration of the product, NO2(g), and decreasing the concentration of the reactant, N2O4(g) at equilibrium.
Which two transmembrane proteins are responsible for maintaining the resting membrane potential of neurons (-60 to -70 mV) and how do they achieve this function?
First, the Na+/K+ pump (also known as Na+/K+-ATPase) causes a net efflux of positive charge, hydrolyzing one ATP to transport 3 Na+ ions out of the cell and 2 K+ ions into the cell, thus utilizing active transport to decrease the total number of cations and increase the net negative charge within the cell membrane. Second, the ungated K+ ion channels (also known as K+ leak channels) remain open to constantly allow K+ ions to leak out of the cell (down their concentration gradient; K+ inside cell > K+ outside of cell), thus utilizing passive transport to decrease the total number of K+ cations and increase the net negative charge within the cell membrane.