Q = I × t : Quantity of Charge (Electricity) Calculations Chemistry Tutorial

Key Concepts

• A galvanic cell (voltaic cell) produces a flow of electrons.

  This flow of electrons is called an electric current.
  Current is given the symbol I and is measured in units of amperes (amps, A).

• The amount of charge passing a point in an electric circuit depends on the electric current and the time the current is allowed to flow for.

  The amount of charge is given the symbol Q and is measured in units of coulombs (C).

• The quantity of charge (or electricity) contained in a current running for a specified time can be calculated:

  Q = I × t
      Q = quantity of charge (electricity) in coulombs (C)
      I = current in amperes (amps, A)
      t = time (seconds)

• This equation can be rearranged to calculate the electric current given quantity of charge (electricity) and time:

  I = Q ÷ t

• This equation can be rearranged to calculate the time taken given the quantity of charge (electricity) and the electric current:

  t = Q ÷ I

• This equation can be used to determine the quantity of charge, electric current, or length of time required to run an electrolysis experiment such as:

  (i) for electroplating
  Example from industry: electrorefining of copper

  (ii) electrolysis of molten salts to extract a metal
  Example from industry: extraction of aluminium from bauxite
  Example from industry: extraction of sodium from molten soduim chloride

  (iii) electrolysis of aqueous solutions to extract an element:
  Example from industry: electrowinning of copper

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Worked Example: Calculating Quantity of Charge

Question: Calculate the quantity of charge (electricity), Q, obtained when a current of 25 amps runs for 1 minute.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

   Calculate the quantity of charge
   Q = ? C

2. What data (information) have you been given in the question?

   Extract the data from the question:
   I = current = 25 A
   t = time = 1 minute
   Convert time in minutes to time in seconds by multiplying by 60
   t = 1 min × 60 sec/min = 60 seconds

3. What is the relationship between what you know and what you need to find out?

   Write the equation: Q = I × t

4. Substitute the values into the equation and solve for Q:

   Q = 25 × 60
     = 1,500 C

5. Is your answer plausible?

   Work backwards: Use your calculated value for Q and the current given in the question to calculate time, then compare this to the time given in the question:
   Q = 1500 C
   I = 25 A

   t = Q ÷ I = 1500 ÷ 25 = 60 seconds
   60 seconds = 1 minute

   Since the time calculated here agrees with that given in the question we are reasonably confident that our answer for Q is correct.

6. State your solution to the problem "calculate quantity of charge":

   Q = 1,500 C

Worked Example: Calculating Current

Question: Calculate the current needed to provide 30,000 coulombs of charge (electricity) in 5 minutes.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

   Calculate the current
   I = ? A

2. What data (information) have you been given in the question?

   Extract the data from the question:
   Q = 30,000 C
   t = 5 minutes
   Convert time in minutes to time in seconds by multiplying by 60
   t = 5 min × 60 sec/min = 300 seconds

3. What is the relationship between what you know and what you need to find out?

   Write the equation: I = Q ÷ t

4. Substitute in the values and solve for I:

   I = Q ÷ t
     = 30,000 ÷ 300
     = 100 amps

5. Is your answer plausible?

   Work backwards: Use the value for the current calculated above and the quantity of charge (electricity) given in the question to calculate the time taken, and compare this to the time given in the question:
   I = 100 A
   Q = 30,000 C

   t = Q ÷ I = 30,000 ÷ 100 = 300 seconds
   Convert time in seconds to time in minutes by dividing by 60
   t = 300 sec ÷ 60 sec/min = 5 minutes

   Since the time calculated here is the same as that given in the question, we are confident that our calculated value for the current is correct.

6. State your solution to the problem "calculate current":

   I = 100 A

Worked Example: Calculating Time

Question: Calculate the time in minutes required to produce 12,000 C of charge (electricity) using a current of 10 amps.

Solution:

(Based on the StoPGoPS approach to problem solving.)

1. What is the question asking you to do?

   Calculate the time in minutes
   t = ? minutes

2. What data (information) have you been given in the question?

   Extract the data from the question:
   Q = 12,000 C
   I = 10 A

3. What is the relationship between what you know and what you need to find out?

   Write the equation: t = Q ÷ I

4. Substitute in the values and solve for t:

   t = Q ÷ I
     = 12,000 ÷ 10
     = 1,200 seconds

   Convert time in seconds to time in minutes by dividing by 60
   t = 1,200 sec ÷ 60 sec/min
     = 20 minutes

5. Is your answer plausible?

   Work backwards: use your calculated value for time and the current given in the question to calculate the quantity of charge and compare this value to that given in the question:
   t = 20 minutes = 20 × 60 = 1200 seconds
   I = 10 A
   Q = I × t = 10 × 1200 = 12,000 C

   Since the value for Q calculated here agrees with the value given in the question we are confident our calculated value for time is correct.

6. State your solution to the problem "calculate time in minutes":

   t = 20 minutes