Assume electricity cost 15 cents kw per hour....using the energy requirements.what is the per gram cost of energy to produce Na + AL?
Useful info: 2NaCL --> 2Na + CL2
around 600 degree C; 14 KJ per g Na.
Al-
2Al2O3-->4Al+3O2
1000 degrees C; 30 KJ per g Al
in cryalite (Na3AlF6) so can be liquid below Tm~2000 degrees C
The 15 cents you quoted would be per kilowatt-hour, not per kw/hour. Energy is the product of power and time.
For Na, if you need 14,000 J of electricity to make 1 gram, then make the conversions 14,000 J = 14,000 Watt-second= 14 kw-second = 14/3600 kw-hour = 0.00389 kw-hour
The cost would be 15 cents/kwh x 0.00389 kwh = 0.058 cents
Do the aluminum question the same way.
To calculate the cost of energy per gram of Na (sodium) and Al (aluminum), we need to consider the energy requirements for their production and the electricity cost. Let's start with sodium.
From the given information, we know that it takes 14 kJ (kilojoules) of energy to produce 1 gram of sodium. To convert kJ to watt-hours (Wh), we need to know the conversion factor. 1 kJ is equal to 1000 J (joules), and 1 Watt-hour (Wh) is equal to 3600 J.
Therefore, the conversion factor is: 14 kJ = 14,000 J = 14,000 Watt-seconds = 14,000/3600 Wh = 3.89 Wh.
Now, considering the electricity cost of 15 cents per kilowatt-hour (kWh), we need to convert the Wh to kWh. Since 1 kWh is equal to 1000 Wh, we divide 3.89 Wh by 1000 to get it in kWh.
3.89 Wh = 3.89/1000 kWh = 0.00389 kWh.
To calculate the cost, we multiply the energy consumed (0.00389 kWh) by the cost per kWh (15 cents).
Cost = 0.00389 kWh * 15 cents/kWh = 0.05835 cents.
Therefore, the cost to produce 1 gram of sodium is approximately 0.05835 cents.
Now let's move on to aluminum.
We are given that it takes 30 kJ of energy to produce 1 gram of aluminum. Using the same process as before, we convert 30 kJ to 8.33 Wh.
Next, we convert Wh to kWh by dividing by 1000: 8.33 Wh = 8.33/1000 kWh = 0.00833 kWh.
Again, multiplying the energy consumed (0.00833 kWh) by the cost per kWh (15 cents), we can calculate the cost.
Cost = 0.00833 kWh * 15 cents/kWh = 0.12495 cents.
Therefore, the cost to produce 1 gram of aluminum is approximately 0.12495 cents.
In summary:
- The per gram cost of energy to produce Na (sodium) is approximately 0.05835 cents.
- The per gram cost of energy to produce Al (aluminum) is approximately 0.12495 cents.