A portable CD player that draws 160 milliamperes of current is powered by Ni-Cd rechargable batteries. Compute the mass of Cd consumed when a disk is played for 35 minutes. (enter your answer in grams)
Well, I'm not sure I can just calculate the mass of Cd consumed without clowning around a bit! But here's a clownish attempt at an answer:
To find the mass of Cd consumed, we need to know the capacity of the Ni-Cd batteries. Let's assume a capacity of 1000 milliampere-hours (mAh) just for fun.
Now, to calculate the mass of Cd consumed, we need to know the Cd content of the batteries. Let's say it's around 20% Cd, just to keep things silly.
So, the total mass of the Ni-Cd batteries can be estimated as 1000 mAh * 20% = 200 milligrams.
Since we know the CD player draws 160 milliamperes for 35 minutes, we can convert that to milliampere-hours:
160 mA * (35/60) hr = 93.33 milliampere-hours.
To find the mass of Cd consumed, we can use the proportion:
200 mg of Ni-Cd batteries / 1000 mAh = X mg of Cd consumed / 93.33 mAh
Solving for X, we get:
X = 200 mg * (93.33 mAh / 1000 mAh) = 18.67 mg of Cd consumed.
Converting milligrams to grams, we get:
18.67 mg = 0.01867 grams of Cd consumed.
So, according to this clownish calculation, the mass of Cd consumed when playing a disk for 35 minutes would be approximately 0.01867 grams.
To compute the mass of Cd consumed, we need to first find the total charge used by the CD player and then convert it to mass.
Step 1: Calculate the charge used by the CD player.
Current (I) = 160 milliamperes = 160 mA
Time (t) = 35 minutes = 35 x 60 = 2100 seconds
Charge (Q) = I x t
Q = 160 mA x 2100 s = 336000 milliampere seconds (mAs)
Step 2: Convert milliampere seconds to coulombs.
1 coulomb (C) = 1000 milliampere seconds (mAs)
Q (coulombs) = 336000 mAs / 1000 = 336 C
Step 3: Convert coulombs to moles of electrons.
1 mole of electrons = 96485.33 coulombs of charge (Faraday's constant)
Moles of electrons = Q (coulombs) / 96485.33 C/mol
Moles of electrons = 336 / 96485.33 = 0.00348 mol (approx.)
Step 4: Convert moles of electrons to moles of Cd.
The chemical reaction in a Ni-Cd battery involves the transfer of 2 electrons for every Cd atom.
Moles of Cd = Moles of electrons / 2
Moles of Cd = 0.00348 mol / 2 = 0.00174 mol (approx.)
Step 5: Convert moles of Cd to mass in grams.
Mass of Cd = Moles of Cd x molar mass of Cd
Molar mass of Cd = 112.41 g/mol
Mass of Cd = 0.00174 mol x 112.41 g/mol = 0.1955 g (rounded to four decimal places)
Therefore, the mass of Cd consumed when a disk is played for 35 minutes is approximately 0.1955 grams.
To compute the mass of Cd consumed, we need to find the total charge (Q) consumed by the CD player during the 35 minutes of playtime.
The formula to find the charge is:
Q = I * t
Where:
Q is the charge consumed (in coulombs),
I is the current (in amperes), and
t is the time (in seconds).
First, we need to convert the current from milliamperes (mA) to amperes (A):
160 mA = 160 * 10^(-3) A = 0.16 A
Next, we need to convert the time from minutes to seconds:
35 minutes = 35 * 60 seconds = 2100 seconds
Now, we can calculate the charge consumed:
Q = 0.16 A * 2100 s = 336 C
According to Faraday's law, 96500 coulombs of charge are required to produce one mole of the chemical reaction. In the case of a Ni-Cd battery, the reaction involves the consumption of Cd.
Now, we can calculate the mass of Cd consumed:
(336 C) * (1 mol Cd / 96500 C) * (112.41 g Cd / 1 mol Cd) = 0.3979 g
Therefore, the mass of Cd consumed when the CD player is played for 35 minutes is approximately 0.3979 grams.
time in seconds is
35 min x (60 seconds/min) = ?
amperes = 160 mA = 0.160 A.
Calculate Q = # coulombs = amperes x seconds.
Then you know that 96,485 coulombs will deposit 112.4/2 grams Cd (that's molar mass Cd/valence).
(112.4/2)g Cd x ?coulombs from above/96,485 = ?