G Currell & A A Dowman, Wiley-Blackwell, 2009

- The pressure,
*p*(Pa), of a fixed volume of a gas is measured as a function of the temperature,*T*(K), and five experimental data values are recorded in the table below.

However, it is thought that there might be a systematic (constant) error in the value for pressure.

The ratio ofData 1 2 3 4 5 Averages *T*(K)273 323 373 423 473 373 *p*(Pa)4400 5000 6400 6900 7000 5940 *p/T*=16.12 15.48 17.16 16.31 14.80 15.97 *p/T*is calculated for each data point, and the average of these is calculated in the last column. The separate averages of all values of*p*and*T*are also calculated.

Given that, for an ideal gas, the concentration is given by*C*= (*p/T*)*/R*,**which would be the best method of analysing the data**to calculate the concentration,*C*, of the gas, assuming it to behave as an ideal gas with*R*= 8.314 J mol^{-1}K^{-1}?- Calculate the ratio of the averages for
*p*and*T*(= 5940 / 373 = 15.92) and then divide by*R*to get 1.915 mol m^{-3}. - Take the average of the
*p/T*ratios (=15.97) and then divide by*R*to get 1.921 mol m^{-3}. - Plot a graph of
*p*against*T*and draw a best-fit straight line which also passes through the origin of the graph. Divide the slope (=15.87) of the line by*R*to get 1.909 mol m^{-3}. - Plot a graph of
*p*against*T*and draw a best-fit straight line which does not have to pass through the origin of the graph. Divide the slope (=14.20) of the line by*R*to get 1.708 mol m^{-3}.

- Calculate the ratio of the averages for
- In a laboratory exercise a student measures the pressure,
*p*_{1}= 7.93 kPa, for a fixed volume of gas at a temperature,*T*_{1}, and then increases the temperature by 50 C and records the new pressure,*p*_{2}= 9.26 kPa. The student failed to record the value of the initial temperature,*T*_{1}, but needs to calculate the concentration of the gas.**Which of the following is true?**

(The ideal gas equation is*pV*=*nRT*and the concentration is given by*C*=*n/V*, with*R*= 8.314 J mol^{-1}K^{-1})- Without the value of
*T*_{1}, it is not possible to calculate the concentration of the gas. - The concentration can be calculated as
*C*= 3.2 mol m^{-3}. - The concentration can be calculated as
*C*= 0.31 mol m^{-3}. - None of the above

- Without the value of
- The equation to describe the pressure,
*p*(kPa), as a function of temperature,*T*_{K}(K), for 3.0 mol of an ideal gas in a fixed volume of 5.0 dm^{3}, is given by:*p*= 4.99×*T*_{K}.

Which of the following would describe the pressure of the same gas as a function of temperature,*T*_{C}(C)?- p = 4.99×
*T*_{C}+ 1.36×10^{3} - p = 4.99×
*T*_{C}- 1.36×10^{3} - p = 499×
*T*_{C}+ 273 - p = 4.99×
*T*_{C}- 273

- p = 4.99×
- The graph shows the experimental variation of pressure,
*p*(kPa), of an ideal gas as a function of temperature,*T*(C).

Estimate, from the best-fit straight line, the concentration of the gas.

Which of the following values is closest to your estimate?

(The ideal gas equation is*pV*=*nRT*and the concentration is given by*C*=*n/V*, with*R*= 8.314 J mol^{-1}K^{-1})- 9.2×10
^{-4}mol m^{-3} - 0.95 mol m
^{-3} - 0.99 mol m
^{-3} - 9.9 ×10
^{-4}mol m^{-3}

- 9.2×10
- The pressure,
*p*(Pa), of a fixed volume of a gas is measured as a function of the temperature,*T*(K). Excel is used to calculate the slope and intercept of the best-fit line of*p*versus*T*, and produces the following results:

Which of the following statements is a correct interpretation of these results?Value Standard Error Intercept -75 135 Slope 10.11 0.33 - The results are NOT consistent with ideal gas behaviour because the intercept is not zero.
- The results are NOT consistent with ideal gas behaviour because the error in the intercept is greater than the error in the slope.
- The results ARE consistent with ideal gas behaviour because a zero intercept is within the uncertainty range of the results.
- The results ARE consistent with ideal gas behaviour because the relative error in the slope is much smaller than the relative error in the intercept.