Chemistry 2710 Spring 2001 Assignment 1

Due: Friday, Jan. 12, 9:00a.m.

1.

Evaluate the following derivatives: [2 marks each]

(a)

$$\frac{d}{dx}\left(x^2+x^{-2}\right)$$

(b)

$$\frac{d}{dt}e^{-kt}$$

2.

Evaluate the following integrals: [3 marks each]

(a)

$$\int_{a_0}^{a(t)}\frac{dx}{x^n}$$, $n\not= 1$

(b)

$$\int_3^{15}\frac{dx}{x}$$ In this case, simplify your answer as much as possible, but do not convert it to a floating-point value.

3.

Disulfur dichloride ( S₂Cl₂) is used to vulcanize rubber. It is made by the following reaction:

$$\mathrm{S}_{8\mathrm{(l)}} + 4\mathrm{Cl}_{2\mathrm{(g)}} \rightarrow 4 \mathrm{S}_2\mathrm{Cl}_{2\mathrm{(l)}}.$$

(a)

If 32.0g of sulfur react with 71.0g of chlorine and assuming the reaction goes to completion, what mass of disulfur dichloride could be obtained? [6 marks]

(b)

If the chlorine is initially held at a pressure of 90kPa and a temperature of $50^\circ\mathrm{C}$, what volume does it occupy? [3 marks]

4.

Suppose that HF gas reacts with aluminium metal. The products are AlF_3(s) and hydrogen gas. Calculate the standard changes in enthalpy and entropy in this reaction. [6 marks]

Substance	$\Delta\bar{H}^\circ_f$	$\bar{S}^\circ$
	(kJ/mol)	(JK-1mol-1)
Al(s)	0	28.30
AlF3(s)	-1510.4	66.5
H2(g)	0	130.680
HF(g)	-273.30	173.779

5.

Find the line of best fit through the following points by linear regression: [4 marks]

x	0.9	1.8	2.5	3.7	4.6
y	3.4	5.5	7.2	10.1	12.2