MC test: Graphical techniques

Multiple choice test on 11.2 Graphical techniques

Use the following 'quiz' to test your knowledge and understanding of this sub-topic. You will need access to a periodic table (Section 6 of the IB data booklet).

If you get an answer wrong, read through the explanation carefully to learn from your mistakes.

Which graph shows the correct relationship between volume and temperature for a fixed mass of an ideal gas at constant pressure?

Volume is directly proportional to the absolute temperature so the intercept (when V = 0 cm3) will be at − 273 oC when the temperature units are oC.

 

Which plot will give a straight line for a fixed mass of an ideal gas?

PV = nRT so P against T will give a straight line.

 

Which lines can be expressed mathematically in the form y = mx + c?

I. 

II. 

III. 

The scale for concentration is not linear.

 

The graph shows the relationship between volume and pressure for a fixed mass of a gas at a constant temperature. How can the graph be used to find the volume of the gas when the pressure is 3.5 x 102 kPa ? 

Interpolation is used when the value required lies within the parameters of the plotted graph.

 

Which are correct about sketch graphs?

I. They communicate the effect of an independent variable on a dependent variable.

II. They have labelled axes.

III. They have unscaled axes.

Sketched graphs have labelled but unscaled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional.

 

The graph shows how the volume of an ideal gas increases as the temperature is increased. How can the graph be used to find the value of absolute zero in degrees Celsius ?

Absolute zero can be obtained by extrapolating the graph until the volume is equal to zero and measuring the intercept on the temperature axis.

 

The graph shows how the concentration of a reactant changes as a reaction proceeds. How can the graph be used to measure the rate of the reaction after it has been proceeding for 7.5 minutes?

 

The rate (in terms of change in concentration of reactant over time in mol dm−3 min−1) will be equal to the gradient of the graph when the time is equal to 7.5 minutes.

 

50.0 cm3 of 0.200 mol dm−3 copper(II) sulfate solution was placed in a polystyrene cup. After 2 minutes excess zinc powder was added and the mixture continually stirred. The following graph was obtained by measuring the temperature every 30 seconds for 16 minutes.

After taking heat loss to the surroundings into account, what value should be used for the temperature rise?

The graph should be extrapolated back to give the temperature at 2 minutes if all the heat had been given out immediately with no heat loss (27.5 oC) and then the initial temperature (17.0 oC) subtracted.

 

50.0 cm3 of 0.200 mol dm−3 copper(II) sulfate solution was placed in a polystyrene cup. After 2 minutes excess zinc powder was added and the mixture continually stirred. The following graph was obtained by measuring the temperature every 30 seconds for 16 minutes.

Which statement best describes what was happening at 6.5 minutes (4.5 minutes after the zinc was added)?

All the time the temperature is increasing above the initial temperature of 17 oC the solution loses heat to the surroundings. While more heat is given out than is being lost the temperature will continue to increase. The highest temperature will be reached when the rate of heat being given out from the reaction is equal to the rate of heat loss to the surroundings. This occurs 4.5 minutes after the zinc was added.

 

Hydrogen reacts with nitrogen monoxide to give steam and nitrogen.

2H2(g) + 2NO(g) → 2H2O(g) + N2(g)

Experimentally it has been shown that the rate of this reaction = k[H2(g)][NO(g)]2 where k is known as the rate constant. As the temperature increases the value of k increases. It can be shown that lnk = −Ea/RT + A, where Ea is the activation energy for the reaction, R is the gas constant,  T is the temperature in Kelvin and A is a constant.

Which graph should be plotted to obtain the value of the activation energy for this reaction directly from the gradient?

Although it is normal to plot lnk against 1/T to give a gradient = −Ea/R, in order to obtain Ea directly, lnk should be plotted against 1/RT.
Knowledge of the use of rate constants and the expression lnk = −Ea/RT + A is not required for standard level but from the information given in the question, SL students should be able to determine which graph to plot to give a straight line with the relevant gradient.

 

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