Studdy AI Logo
Math

QuestionCalculate the time to deposit 0.50 g of gold (atomic mass 197) using a current of 0.10 A and Faraday's constant F=96485CF = 96485 \mathrm{C}.

Studdy Solution

STEP 1

Assumptions1. The atomic mass of gold is197 g/mol. The amount of gold to be deposited is0.50 g3. The current passed is0.10 Faraday () 4.1 Faraday is equivalent to96485 Coulombs (C)
5. The time required to deposit the gold is what we need to find6. The Faraday's law of electrolysis states that the amount of substance deposited or dissolved at any electrode is directly proportional to the quantity of electricity passed through the electrolyte.

STEP 2

First, we need to find the number of moles of gold to be deposited. We can do this by dividing the mass of gold by its atomic mass.
Moles of gold=Mass of goldAtomic mass of gold\text{Moles of gold} = \frac{\text{Mass of gold}}{\text{Atomic mass of gold}}

STEP 3

Now, plug in the given values for the mass of gold and the atomic mass of gold to calculate the moles of gold.
Moles of gold=0.50 g197 g/mol\text{Moles of gold} = \frac{0.50 \, \text{g}}{197 \, \text{g/mol}}

STEP 4

Calculate the moles of gold.
Moles of gold=0.50197=0.00254 mol\text{Moles of gold} = \frac{0.50}{197} =0.00254 \, \text{mol}

STEP 5

Now, we need to find the number of Faradays required to deposit the gold. According to Faraday's law of electrolysis,1 mole of a substance requires1 Faraday to deposit. So, the number of Faradays is equal to the number of moles of gold.
Faradays required=Moles of gold\text{Faradays required} = \text{Moles of gold}

STEP 6

Now, plug in the value for the moles of gold to find the Faradays required.
Faradays required=0.00254 \text{Faradays required} =0.00254 \, \text{}

STEP 7

Next, we need to find the time required to deposit the gold. We can do this by dividing the Faradays required by the current passed.
Time required=Faradays requiredCurrent passed\text{Time required} = \frac{\text{Faradays required}}{\text{Current passed}}

STEP 8

Now, plug in the values for the Faradays required and the current passed to calculate the time required.
Time required=0.00254 0.10 /s\text{Time required} = \frac{0.00254 \, \text{}}{0.10 \, \text{/s}}

STEP 9

Calculate the time required.
Time required=.00254.=.0254 s\text{Time required} = \frac{.00254}{.} =.0254 \, \text{s}However, the time given in the problem is in seconds, so we need to convert our time from Faradays to seconds.

STEP 10

We know that Faraday is equivalent to96485 Coulombs (C), and Coulomb per second is equivalent to Ampere (A). Therefore, we can convert the time from Faradays to seconds by multiplying by the conversion factor.
Time required=0.0254 ×96485 C × s C\text{Time required} =0.0254 \, \text{} \times \frac{96485 \, \text{C}}{ \, \text{}} \times \frac{ \, \text{s}}{ \, \text{C}}

STEP 11

Calculate the time required in seconds.
Time required=0.0254×96485=245.4 s\text{Time required} =0.0254 \times96485 =245.4 \, \text{s}So, it will take approximately245.4 seconds to deposit0.50 g of gold.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord