1.0 mol of water (c=4.184 J/g.oC), 1.0 mol of ethanol (c=2.46 J/g.oC), 1.0 mol of carbon tetrachloride (c=0.861 J/g.oC), and 1.0 mol of ethylene glycol (c=2.42 J/g.oC) at 50oC were each placed into a separate coffee cup calorimeter and the temperature recorded. The temperature of the surroundings was 20oC. After 1 hour the temperature of which substance would have changed by the smallest amount? Assume the rate of heat transfer from the coffee cup to the surroundings is the same in each case.
heat in cup= mass*specific heat*temp difference.
temp in cup= (heatinitially-heatlost(t))/(mass*c)
temp in cup= Ti- heat lost(t)/m*c
so since the heat lost (t) is the same for all cups, the temp in the cup depends on massstuff*c
look at the products of massmole*c for each of the four combinations. To get the lowest temp change, mc product has to be high.
To determine which substance's temperature would have changed by the smallest amount after 1 hour, we can use the principle of heat transfer and calculate the change in temperature using the formula:
q = mcΔT
where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
Since we are given that 1.0 mol of each substance is used, we can assume the same mass for each. However, we need to convert the moles to grams using the molar mass of each substance.
The molar mass of water (H2O) is approximately 18.015 g/mol.
The molar mass of ethanol (C2H5OH) is approximately 46.07 g/mol.
The molar mass of carbon tetrachloride (CCl4) is approximately 153.823 g/mol.
The molar mass of ethylene glycol (C2H6O2) is approximately 62.07 g/mol.
Now, we can calculate the heat transfer for each substance based on the given specific heat capacities:
For water:
q = (1.0 mol) * (18.015 g/mol) * (4.184 J/g.oC) * (50oC - 20oC)
For ethanol:
q = (1.0 mol) * (46.07 g/mol) * (2.46 J/g.oC) * (50oC - 20oC)
For carbon tetrachloride:
q = (1.0 mol) * (153.823 g/mol) * (0.861 J/g.oC) * (50oC - 20oC)
For ethylene glycol:
q = (1.0 mol) * (62.07 g/mol) * (2.42 J/g.oC) * (50oC - 20oC)
By calculating the values, we find that the value of q (heat transferred) is the smallest for carbon tetrachloride. Hence, the temperature of carbon tetrachloride would have changed by the smallest amount after 1 hour.