Please help I am desperate!!
INSTRUCTIONS:
MOXIE has already passed the preliminary design review and is now scheduled for critical
design review. You are a chemical engineer working for NASA and your job is to monitor and
analyze data from processes and identify ways to optimize performance.
Upon receiving the prototype tank at your facility, you read “rupture pressure of 78 atm” on the tank. Knowing that Mars follows a highly elliptical orbit, and thus temperatures vary significantly as the planet travels around the Sun, you take it upon yourself to validate JFK Tank and Manufacturing Co.’s statement “designed to meet a wide range of requirements...” and review the behaviour of gases.
Mars Information:
- Pressure is approximately 0.02 atm.
- Temperature in winter is 133 K
- Temperature in summer is 294 K
1. If the Moxie's tank has an initial pressure of 50 atm in the winter, what will be the pressure in the summer?
- 5.88 atm
- 22.6 atm
- 110.5 atm
2. Can the tank withstand the change from winter to summer if it has 50 atm of pressure initially?
- Yes
- No
3. Scientists want to store the converted oxygen into tanks on Mars' surface. What would be the maximum temperature the tanks could reach if it was known at 133 K their minimum volume would be 25 L and their maximum volume could not exceed 54 L without rupturing
- 62 K
- 10 K
- 287 K
4. Would this size of tank be able to withstand the summer temperatures on Mars?
- Yes
- No
5. The Moxie will be converting CO2 to O2. It is being constructed and tested on Earth. However, scientists must take into account the lower atmospheric pressure of Mars. If the Moxie can store on 22.5 L of O2 on Earth (1 atm), what would happen to the volume when the tank was placed on the surface of Mars?
- It would crush inwards with a volume of 0.45 L
- It would explode outwards with a volume of 1, 125 L
6. The 1.98-L storage tank has a listed capacity of 215 g of O2. Use the ideal gas law to calculate the pressure of the storage tank at 20 C (the peak daytime temperature on Mars).
- 81.6 atm
- 0.02 atm
- 178 atm
7. Is the O2 tank safe against sudden rupture at capacity?
- Yes, it will be fine.
- Nope, she is going to blow.
8. Currently the rover, Perseverance, is on Mars and collecting data. Recently, it sent data to NASA regarding its hydraulic cylinders that operate the camera. The rigid cylinder has a volume of 0.75 L. On day 1 of landing on the red planet the temperature was 157 K. By day 100, the temperature had increased by 37 K. If the initial pressure in the hydraulic system was 3.5 kPa, what is the pressure on day 100?
- 0.83 kPa
- 2.83 kPa
- 4.32 kPa
9. How might the world be different if all gases behaved ideally?
Nine (9) questions here and I see no effort on your part. Apparently you can type but you don't want to think. You may be desperate but I'm not stupid. The idea here is to HELP you. It is NOT to do ALL of your work. You show me some work and I'll help. Info is
- Pressure is approximately 0.02 atm.( what does this mean?
- Temperature in winter is 133 K
- Temperature in summer is 294 K
For question 1 use (P1/T1) = (P2/T2)
P1 = 50 atm in the winter (so T1 = 133 from the problem.
T2 = summer T = 294
(50/133) = (P2/294) and solve for P2.
P2 is 110.5 atm so the answer is c.
Note: The answer in the problem isn't QUITE right for there are four significant figures in the answer and you're only allowed 3 so the answer SHOULD HAVE BEEN shown as 110 atm
Good luck on the others. Show me some work or tell me why you're stuck and I'll help further.
1. To calculate the pressure in the summer, we can use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since the initial pressure in the winter is 50 atm and the final pressure in the summer is unknown, we can set up the equation as follows:
(50 atm)(V1) = (n)(R)(133 K)
Similarly, for the summer conditions:
(P2)(V1) = (n)(R)(294 K)
To find the pressure in the summer, we can rearrange this equation:
P2 = (50 atm)(294 K) / (133 K)
Calculating this, we find that the pressure in the summer is approximately 110.5 atm.
Therefore, the answer to question 1 is:
- 110.5 atm
2. To determine if the tank can withstand the change from winter to summer, we need to compare the pressure change to the rupture pressure of the tank.
The pressure change from winter to summer is 60.5 atm (110.5 atm - 50 atm). Since 60.5 atm is less than the rupture pressure of 78 atm, the tank can withstand the change.
Therefore, the answer to question 2 is:
- Yes
3. To find the maximum temperature the tanks could reach, we need to compare the volume change to the given minimum and maximum volumes.
Using the ideal gas law equation again, we can calculate the maximum temperature:
P1V1 / T1 = P2V2 / T2
We know the following values:
P1 = 0.02 atm
V1 = 25 L
T1 = 133 K
V2 = 54 L
Solving for T2:
T2 = (P1V1 T2) / (P2V2)
T2 = ( (0.02 atm)(25 L) (287 K) ) / ( (54 L) )
T2 ≈ 287 K
Therefore, the answer to question 3 is:
- 287 K
4. Since the maximum temperature the tanks could reach on Mars is 287 K, and the summer temperature on Mars is 294 K, the tank can withstand the summer temperatures.
Therefore, the answer to question 4 is:
- Yes
5. To determine the volume change when the tank is placed on the surface of Mars, we can use the ideal gas law equation again.
Using the inverse of Boyle's Law, which states that P1V1 = P2V2, we can calculate the new volume on Mars using the given information.
The initial volume on Earth is 22.5 L at 1 atm. On Mars, the pressure is approximately 0.02 atm.
Using the equation:
(1 atm)(22.5 L) = (0.02 atm)(V2)
V2 = (1 atm)(22.5 L) / (0.02 atm)
V2 = 1125 L
Therefore, the answer to question 5 is:
- It would explode outwards with a volume of 1,125 L
6. To calculate the pressure in the storage tank, we can use the ideal gas law equation again.
Given:
V = 1.98 L
m = 215 g
R = 0.0821 atm L/mol K
T = 20°C = 293 K
Rearranging the ideal gas law equation to solve for pressure, we have:
PV = nRT
First, we need to calculate the number of moles (n) using the mass of oxygen:
n = m/M, where M is the molar mass of oxygen (32 g/mol)
n = 215 g / 32 g/mol ≈ 6.72 mol
Substituting the values into the equation, we get:
P(1.98 L) = (6.72 mol)(0.0821 atm L/mol K)(293 K)
Simplifying and solving, we find that the pressure in the storage tank is approximately 81.6 atm.
Therefore, the answer to question 6 is:
- 81.6 atm
7. To determine if the O2 tank is safe against sudden rupture at capacity, we need to compare the pressure to the rupture pressure of the tank, which is not provided.
Without the rupture pressure information, we cannot confidently answer this question. Please check the given information for any additional details.
Therefore, the answer to question 7 is:
- Insufficient information
8. To find the pressure on day 100, we can use the ideal gas law equation.
Given:
V1 = 0.75 L
T1 = 157 K
T2 = 157 K + 37 K = 194 K (increase in temperature)
Using the equation:
(P1)(V1) / T1 = (P2)(V2) / T2
Substituting the values, we have:
(3.5 kPa)(0.75 L) / (157 K) = (P2)(0.75 L) / (194 K)
Simplifying and solving for P2, we find that the pressure on day 100 is approximately 2.83 kPa.
Therefore, the answer to question 8 is:
- 2.83 kPa
9. If all gases behaved ideally, several differences in the world could occur:
- Gas transport and storage would be more predictable and easier to control.
- Ideal gas laws would accurately describe the behavior of gases in various conditions.
- Chemical reactions involving gases would follow ideal gas laws.
- Measurements and calculations involving gases would be simpler and more consistent.
These are just a few examples of how the world would be different if all gases behaved ideally. The behavior of gases in real-world conditions often deviates from ideal gas behavior due to factors such as intermolecular interactions and non-ideal conditions.
Therefore, the answer to question 9 is:
- Gas transport and storage would be more predictable and easier to control. Ideal gas laws would accurately describe the behavior of gases in various conditions.
To answer these questions, we will use the ideal gas law, which states the relationship between pressure (P), volume (V), temperature (T), and the number of moles of gas (n). The ideal gas law equation is:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
Let's start answering the questions:
1. If the Moxie's tank has an initial pressure of 50 atm in the winter, what will be the pressure in the summer?
To answer this question, we need to use the ideal gas law equation. We know the initial pressure in the winter (P1 = 50 atm), the final pressure in the summer (P2), and the initial and final temperatures (T1 = 133 K and T2 = 294 K, respectively). Assuming the number of moles of gas and the volume remain constant, we can write the equation:
P1V1 / T1 = P2V2 / T2
Since the volume doesn't change, we can simplify the equation to:
P1 / T1 = P2 / T2
Now we can substitute the known values and solve for P2:
50 atm / 133 K = P2 / 294 K
P2 = 50 atm * 294 K / 133 K
P2 ≈ 110.5 atm
Therefore, the pressure in the summer would be approximately 110.5 atm.
Answer: 110.5 atm
2. Can the tank withstand the change from winter to summer if it has 50 atm of pressure initially?
To determine if the tank can withstand the pressure change, we need to compare the initial pressure (50 atm) with the rupture pressure of the tank (78 atm) as stated on the tank. Since the initial pressure is lower than the rupture pressure, the tank can withstand the change from winter to summer.
Answer: Yes
3. What would be the maximum temperature the tanks could reach if it was known at 133 K their minimum volume would be 25 L and their maximum volume could not exceed 54 L without rupturing?
To answer this question, we need to consider the volume and temperature relationship based on the given information. We can set up the equation using the ideal gas law:
P1V1 / T1 = P2V2 / T2
Since the pressure does not change, we can simplify the equation:
V1 / T1 = V2 / T2
Now, we can substitute the known values (V1 = 25 L, V2 = 54 L, and T1 = 133 K) and solve for T2:
25 L / 133 K = 54 L / T2
T2 = 54 L * 133 K / 25 L
T2 ≈ 287 K
Therefore, the maximum temperature the tanks could reach is approximately 287 K.
Answer: 287 K
4. Would this size of tank be able to withstand the summer temperatures on Mars?
To determine if the tank can withstand the summer temperatures on Mars, we need to compare the maximum temperature (287 K) with the rupture temperature of the tank. However, the rupture temperature of the tank is not given in the information provided. Without this information, we cannot determine if the tank can withstand the summer temperatures.
Answer: Insufficient Information
5. What would happen to the volume of the tank storing O2 (22.5 L at 1 atm on Earth) when placed on the surface of Mars?
To answer this question, we need to consider the change in pressure when the tank is transferred from Earth (at 1 atm) to the surface of Mars (approximately 0.02 atm). We can use the ideal gas law to calculate the new volume (V2) on Mars:
P1V1 = P2V2
Substituting the known values (P1 = 1 atm, V1 = 22.5 L, P2 = 0.02 atm), we can solve for V2:
1 atm * 22.5 L = 0.02 atm * V2
V2 = (1 atm * 22.5 L) / 0.02 atm
V2 = 1125 L
Therefore, the volume of the tank, when placed on the surface of Mars, would be 1125 L.
Answer: It would explode outwards with a volume of 1,125 L
(Note: It is important to note that the given options do not include the correct answer. The correct answer should be "It would increase to 1,125 L.")
6. To calculate the pressure of the storage tank at 20 °C (293 K), we need to use the ideal gas law equation. We know the volume (V = 1.98 L), temperature (T = 20 °C = 293 K), and the number of moles of O2 (n). However, the number of moles is not provided in the information given, so we cannot calculate the pressure without this information.
Answer: Insufficient Information
7. To determine if the O2 tank is safe against sudden rupture at capacity, we need to compare the pressure inside the tank at capacity with the rupture pressure. However, the rupture pressure of the tank is not provided in the information given, so we cannot determine if the tank is safe against sudden rupture.
Answer: Insufficient Information
8. To find the pressure on day 100, we need to calculate the final pressure (P2) using the ideal gas law equation. We know the initial pressure (P1 = 3.5 kPa), the initial volume (V1 = 0.75 L), the initial temperature (T1 = 157 K), and the change in temperature (ΔT = 37 K). Assuming the volume and moles of gas remain constant, we can write the equation:
P1 / T1 = P2 / T2
Since the volume doesn't change, we can simplify the equation to:
P1 = P2 / T2
Now we can substitute the known values and solve for P2:
3.5 kPa = P2 / (157 K + 37 K)
3.5 kPa = P2 / 194 K
P2 = 3.5 kPa * 194 K
P2 ≈ 679 kPa
Therefore, the pressure on day 100 would be approximately 679 kPa.
Answer: 679 kPa
9. Discussing how the world would be different if all gases behaved ideally is subjective and speculative. If all gases behaved ideally, it could simplify calculations and predictions involving gases. However, the behavior of real gases is influenced by various factors, such as intermolecular forces and non-ideal conditions, which can affect their real-world applications.