1 mol of Helium is formed from 2 mol of protons and 2 mol of neutrons. The mass that was lost is 0.0305g. What is the energy change?
A) 9.15 x 10^6 J
B) 2.73 x 10^15 J
C) 9.15 x10^3 J
D) 2.74 x 10^12 J
E) This calculation requires a time period
d
Well, this sounds like a real atom-smashing party. Let's crunch the numbers and find out the energy change!
To calculate the energy change, we can use the famous Einstein's equation: E = mc^2, where E is energy, m is mass, and c is the speed of light (approximately 3 x 10^8 m/s).
First, let's find the mass lost. We know that 1 mole of Helium is formed from 2 moles of protons and 2 moles of neutrons. Since protons and neutrons have roughly the same mass, we can treat it as a 2-2 ratio. Given that the mass lost is 0.0305g, we can divide it by 4 to get the mass loss per particle: 0.0305g / 4 = 0.007625g per proton or neutron.
Now, let's convert this mass loss to kilograms for consistency: 0.007625g = 0.007625 x 10^-3 kg = 7.625 x 10^-6 kg.
Now, let's plug everything into Einstein's equation. E = (7.625 x 10^-6 kg) x (3 x 10^8 m/s)^2.
Calculating it out, the energy change comes out to be approximately 6.8625 x 10^14 J.
But wait! We're not done yet. They asked for the energy change for 1 mole of Helium. So, we need to multiply our answer by Avogadro's number, which is approximately 6.02 x 10^23.
Multiplying 6.8625 x 10^14 J by 6.02 x 10^23, we get approximately 4.13445 x 10^38 J.
Oops! It looks like none of the given options match our calculated result. So, I'm sorry to say, but we don't have a match for this question's answer choices. Let's try not to lose any more mass during our calculations next time, okay?
To determine the energy change, we can use Einstein's mass-energy equivalence equation, E = mc², where E is the energy change, m is the mass lost, and c is the speed of light (approximately 3 x 10^8 m/s).
Given:
Mass lost (m) = 0.0305 g
Speed of light (c) = 3 x 10^8 m/s
First, we need to convert the mass lost (m) from grams to kilograms, as the unit of mass in the equation should be in kilograms.
0.0305 g = 0.0305 / 1000 kg = 0.0000305 kg
Next, we can calculate the energy change using the equation:
E = mc²
E = (0.0000305 kg) * (3 x 10^8 m/s)²
E = 0.0000305 kg * 9 x 10^16 m²/s²
E = 2.75 x 10^12 kg m²/s²
Finally, we can express the energy change in joules by using the definition of the joule:
1 J = 1 kg m²/s²
Therefore, the energy change is approximately 2.75 x 10^12 J.
The correct answer is:
D) 2.74 x 10^12 J
To determine the energy change, we can use Einstein's mass-energy equivalence equation, E = mc^2, where E is the energy change, m is the mass lost, and c is the speed of light.
First, we need to find the mass lost. We know that 1 mole of helium is formed from 2 moles of protons and 2 moles of neutrons. Since protons and neutrons have approximately the same mass, we can assume that the mass of 2 mol of protons and 2 mol of neutrons is equal to the mass of 1 mol of helium.
The molar mass of helium is approximately 4 g/mol, so the mass of 1 mol of helium is 4 grams.
Therefore, the mass lost is 4 g - 4 g + 0.0305 g = 0.0305 g.
Now, we can calculate the energy change using the equation E = mc^2.
E = (0.0305 g) * (3 x 10^8 m/s)^2
E = (0.0305 g) * (9 x 10^16 m^2/s^2)
E = 2.745 x 10^15 g*m^2/s^2
To convert grams to kilograms, we divide by 1000:
E = 2.745 x 10^12 kg*m^2/s^2
Finally, let's convert kg*m^2/s^2 to joules using the conversion factor 1 J = 1 kg*m^2/s^2:
E = 2.745 x 10^12 J
Thus, the energy change is approximately 2.745 x 10^12 J.
D) 2.74 x 10^12 J is the correct answer.