# Tutor profile: Sydney D.

## Questions

### Subject: Chemistry

At a temperature of 290K, hydrogen gas and oxygen gas form water: 2H2(g) + O2 (g) --> 2H2O (l) where H= -285.8kJ/mol and where S= -327 J/Kmol. Is this reaction spontaneous?

For a reaction to be spontaneous, Gibbs free energy must be a negative value. Gibbs's free energy refers to the amount of energy a reaction can use to do work. Gibbs free energy can be calculated using the equation, G = H-TS. H in this equation is enthalpy which for this reaction is -285.8 kJ/mol. When enthalpy of a reaction is negative, it indicates that it is an exothermic reaction/one that releases heat. The T in the equation is the temperature in Kelvin, which in this reaction is 290K. The S in this reaction represents entropy. Entropy is the amount of disorder in a reaction and in this reaction is it negative indicating less disorder is present. In this reaction, the entropy is -327 J/kmol or -0.327kJ/Kmol. If all these values are put into the equation, G = (-285.8kJ/mol) - (290K)(-0.327kJ/Kmol) = -190 kJ/mol. Therefore, the reaction is spontaneous because G is negative.

### Subject: Biology

Explain in detail, how depolarization in a neuron occurs?

In a neuron, there are more K+ ions found inside the cell and more Na+ ions found outside the cell. However, the inside of the neuron is negative due to high amounts of negative proteins. This gives the neuron a charge of -70mV. This charge is called the neuron's resting membrane potential. The Na+ ions want to flow into the cell with their concentration and electrochemical gradient. The concentration gradient refers to the ions wanting to flow where there are fewer of them, so into the cell. The electrochemical gradient refers to how these + ions want to flow into the neuron as it has a negative charge (+ and - attract). Depolarization is when the neuron becomes more positive and moves away from the -70mV charge to one that is +40mV. This occurs when a stimulus causes Na+ channels to open on the neuron's membrane . This is often called achieving action potential. This causes the Na+ ions to rush into the cell leading it to become more positive and therefore the cell is now depolarized.

### Subject: Calculus

A chicken is put in a 300 degrees Celsius oven and heats up according to the differential equation dH/dt = -k (H-300). If the chicken is put in the oven at 20 degrees, solve the differential equation?

dH/dt = -k (H-300) Step 1: Separate the variables by moving them to the appropriate sides of the equation dH/(H-300) = -kdt Step 2: Integrate both sides and make sure to add the constant value C In|H-300| = -kt+ C Step 3: Take the exponential of each side so you can solve for H. e^In will cancel out. e^(In|H-300|) = e^(-kt+C) H -300= e^(-kt+C) H-300 = e^-kt(e^C) Step 4: Let A equal e^C to simplify the equation H-300 = Ae^(-kt) Step 5: When the chicken is put into the oven it is at 20 degreess so at time 0, H =20 H = 300+ Ae^(-kt) 20= 300 +Ae^(-k0) Step 6: Solve for A and put the value back into the equation used in Step 5. A= -280 H = 300 -280e^(-kt)

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