Unit Conversion and Significant Figures in a Chemical Calculation
A student is calculating the number of moles of gas in a 2.50 L container at 25.0 °C and 1.20 atm using the ideal gas law, PV = nRT, where R = 0.08206 L·atm/(mol·K). The student performs the calculation and reports the answer as 0.123 mol. The instructor marks it incorrect due to significant figures and unit errors. The student used 25.0 °C directly as the temperature without converting to Kelvin. The student also used 2.50 L and 1.20 atm, which have three significant figures each. The student needs to correct the calculation and understand the rules for significant figures and unit conversions.
1. Identify the errors in the student's calculation and perform the correct calculation, paying attention to units and significant figures.
Read the worked answer
The student's reported value of 0.123 mol is actually correct if the temperature was converted to Kelvin. However, the student did not show the conversion and may have used 25.0 °C directly in the calculation, which would give n = (1.20 atm × 2.50 L) / (0.08206 L·atm/(mol·K) × 25.0 K) = 1.46 mol, not 0.123 mol. Since the reported value is 0.123 mol, the student likely converted to Kelvin but perhaps used 273 K instead of 273.15 K, which still gives 0.123 mol. The main errors are: (1) not explicitly converting temperature to Kelvin, and (2) not applying significant figures correctly in the intermediate steps. The correct calculation: T = 25.0 °C + 273.15 = 298.15 K, which to the proper number of significant figures (based on 25.0 having one decimal place) is 298.2 K. Then n = PV/(RT) = (1.20 atm × 2.50 L) / (0.08206 L·atm/(mol·K) × 298.2 K) = 3.00 / 24.47 = 0.1226 mol. Rounding to three significant figures (limited by 1.20 and 2.50) gives 0.123 mol. So the student's final answer is correct, but the work should show the temperature conversion and proper significant figures.
2. If the pressure was measured as 1.2 atm instead of 1.20 atm, how would that affect the number of significant figures in the final answer? Recalculate with 1.2 atm.
Read the worked answer
If pressure is 1.2 atm (2 significant figures), then the final answer should have 2 significant figures. Using the same temperature (298.2 K) and volume (2.50 L, 3 sig figs), n = (1.2 × 2.50) / (0.08206 × 298.2) = 3.0 / 24.47 = 0.1226 mol, but with 2 sig figs, it rounds to 0.12 mol. So the answer would be 0.12 mol.