Tutor profile: Gregory K.
Which of the following reactions is most likely to have both a positive ΔH and ΔS? A. heat + NH4Cl (s) → NH3 (g) + HCl (g) B. 2SO2 (g) + O2 (g) → 2SO3 (g) + heat C. heat + H2 (g) + CO2 (g) → H2O(g) + CO(g) D. 2NO (g) → N2 (g) + O2 (g) + heat
To have a positive ΔH the reaction must take in heat energy. This means that heat will go in the reaction, and be stored by the products. Therefore, B and D are eliminated as heat is released from the products having a negative ΔH value. To have a positive ΔS value entropy (disorder) must increase. This occurs when more of an unstable form is created through a reaction e.g. solid to a gas. A has a solid forming two moles of a gas, so disorder increases. However, two moles of a gas react to produce two moles of gas as well. Therefore, it is unlikely that ΔS will be positive in reaction C. This leaves A as the only option, and is the correct answer!
Let us take the function f(x) = 3x^2 + 2x +1 When x = 4, is the function increasing or decreasing? Is the function concave up, or concave down?
To find where a function increases or decreases, the derivative must be found. Differentiating f(x) = 3x^2 +2x +1 will give us that f'(x) = 6x +2. When x=4, f'(4) is equal to 26, so the rate of gradient change is positive and so the curve is increasing at this point. To find whether the curve is concaved up or down, the second derivative must be taken of f'(x). DIfferentiating f'(x) = 6x +2 can be done to find f''(x) = 6. Therefore, having no x variable, the curve is permanently concaved up
Given a positive integer n such that i^n = 1, which of the following statements about n must be true? F. When n is divided by 4, the remainder is 0 G. When n is divided by 4, the remainder is 1 H. When n is divided by 4, the remainder is 2 J. When n is divided by 4, the remainder is 3 K. Cannot be determined from the given information (taken from the "Preparing for the ACT Test" booklet, 2018)
The answer is F! This is due to the fact that i equals the square root of negative one. When i is squared, the value of i^2 is -1. However, we need i^n to equal positive one. Therefore, we multiply i^2 by i^2, simply squaring -1. This gives us the answer that n=4 as n=2+2, so when n is divided by 4 the remained is 0
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