A student in Chemistry wanted to determine the value of R and so used the reaction:

Mg(s) + 2 HCl(aq) → H2(g) + MgCl2 (aq) 

She got a piece of magnesium ribbon and determined its mass as 0.0841 g. She placed the ribbon in a test tube with water and excess HCl and inverted it to allow the H2 gas to bubble to the top of the tube while water was pushed out the bottom. She measured the volume of the gas in the tube as 87.8 mL. She measured the temperature of the water at 20.5?C and the atmospheric pressure in the room was 751 torr.  

 

1- What other piece of information did she have to determine in order to accurately calculate R? 

2- What did she calculate for the value of R? 

3- What was her % error? 

1. Moles of H₂ gas produced are to be determined in order to accurately calculate R.
2. The student calculated the value of gas constant, R to be 0.08445 atm.L.mol^-1.K^-1.
3. The percentage error in the value of R is 2.92 %.

Step-by-step explanation

1.   The given reaction is:

?Mg(s)+2HCl(aq)→H2?(g)+MgCl2?(aq)?

Now as per the reaction 1 mole of Mg forms 1 mole of H₂ gas in excess HCl.

Thus, first calculate the moles of Mg reacted:

Mass of Magnesium ribbon, Mg = 0.0841 g

Molar mass of Mg = 24.305 g/mol

?Moles of Mg = Molar mass of MgMass of Mg?=24.305 g/mol0.0841 g?Moles of Mg =0.0035 moles?

As, moles of H₂ gas produced = moles of magnesium reacted.

thus, moles of H₂ gas produced = 0.0035 moles

Hence, moles of H₂ gas produced are to be determined in order to accurately calculate R.

2.   Ideal gas Law: The equation that relates the pressure (P), temperature (T), Volume (V) and moles (n) of a gas is known as ideal gas law and it is expressed as:

?PV=nRTwhereR is the gas constant?

Now, for the given reaction,

P = 751 torr

?1 Torr = 7601? atm751 Torr =760 Torr/atm751 Torr?=0.988 atm?

T = 20. 5°C = 20.5 + 273 = 293.5 K

V = 87.8 mL = 0.0878 L

Moles of gas, n = 0.0035 moles

Therefore, R is determined as:

?R =nTPV?=(0.0035 moles)×(293.5 K)(0.988 atm)×(0.0878 L)?R= 0.08445 atm.L.mol−1.K−1?

Therefore, the student calculated the value of gas constant, R to be 0.08445 atm.L.mol^-1.K^-1.

3.   Theoretical value of R = 0.08205 atm.L.mol^-1.K^-1

Experimental value of R = 0.08445 atm.L.mol^-1.K^-1

Percentage error is defined as:

?%error =Theoretical valueExperimental value −Theoretical value?×100?

Thus,

?%error=(0.08205atm.L.mol−1.K−1)(0.08445 atm.L.mol−1.K−1)−(0.08205atm.L.mol−1.K−1)?×100%error=(0.08205atm.L.mol−1.K−1)0.0024atm.L.mol−1.K−1?×100%error=2.92%?

Hence, the percentage error in the value of R is 2.92 %.