The vapor pressure of water changes with temperature, as shown here. A student d
ID: 976726 • Letter: T
Question
The vapor pressure of water changes with temperature, as shown here.
A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 2.50 min , 14.7 mL of water-saturated H2(g) is collected. The temperature and pressure of the system are 25 C and 715 torr.
T (C) P (torr) 21 18.7 22 19.8 23 21.1 24 22.4 25 23.8 26 25.2 27 26.7 28 28.4 29 30.0 30 31.8Explanation / Answer
Current is equal to the amount of charge passing through a cross section per unit of time. This is displayed by the following:
I = Q/t, where I is current, Q is total charge passing, and t is time for total charge to pass.
Time is given, but not total charge passing. The total charge is found by knowing the amount of moles of electrons passing. The half reactions and the overall reaction of the electrolysis should be displayed to help find the amount of moles of electrons passing.
2H2O(l) --> O2(g) + 4H+ + 4e-
4H+ + 4e- --> 2H2(g)
2H2O(l) --> 2H2(g) + O2(g)
For every two moles of water oxidizing, four moles of electrons are formed and moving. Using the ideal gas formula, the amount of moles of water oxidized should be found.
PV = nRT, where P is pressure, V is volume, n is moles, R is a constant, and T is temperature.
Isolate moles on one side of the equation and plug in the given values to the rest of the equation. Convert the units appropriately.
n = PV/(RT)
P = 715 torr
P = 715 torr * 1atm/760 torr = 0.9407894737atm
V = 14.7mL
V = 14.7mL * 1L/1000mL = 0.0147L
R = 0.08206L*atm/(mol*K)
T = 25 C
T = 25 C * 1K/1 C + 273.15K = 298.15K
n = (0.9407894737 * 0.0147)/(0.08206 * 298.15)
n = 5.65 * 10-5 mol
This is the amount of moles of water oxidized. Convert this number to the number of moles of electrons produced.
5.65 * 10-5 mol H2O * 4mol electrons/2mol H2O = 1.13 * 10-3 mol electrons
Convert this number to total charge by using avogadro's number and the amount of charge per electron.
1.13 * 10-3 mol electrons * 6.0221413 * 1023 electrons/1mol electrons
1.6 *1 0-19 C/1 electron = 108.89 C
This is the total charge passing through the cross section. Find the current by using the first equation.
I = 108.89 C/3.00 min = 36.29 C/min
Convert this number to amperes.
36.29 C/min * 1min/60s * 1A/(1C/s) = 0.605 A
The magnitude of the electrical current is 0.605 A.
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