A life raft containing 200 g of air has another 200 g of air added.
What happens to the remaining quantities
Pressure (P)
Volume (V)
Moles (n)
Gas constant (R)
Temperature (T)
(doubles / halves / stays constant)
(doubles / halves / stays constant)
(doubles / halves / stays constant)
(doubles / halves / stays constant)
(doubles / halves / stays constant )
The pressure (P) doubles because the mass of air in the life raft doubles, but the volume (V) stays constant as no additional space is added to the life raft. The number of moles (n) stays constant as no air is added or removed. The gas constant (R) and temperature (T) also stay constant as there are no changes to the system.
To determine what happens to the remaining quantities after adding another 200 g of air to a life raft containing 200 g of air, we can use the ideal gas law equation:
PV = nRT
where:
P is the pressure
V is the volume
n is the number of moles
R is the gas constant
T is the temperature
Let's analyze each quantity individually:
1. Pressure (P):
The pressure is directly proportional to the number of moles and the temperature, and inversely proportional to the volume. When the amount of air doubles (from 200 g to 400 g), the number of moles also doubles, assuming the temperature and volume remain constant. Therefore, the pressure will also double.
2. Volume (V):
The volume is inversely proportional to the pressure when the amount of gas and the temperature are constant. Since the pressure doubles, the volume will be halved.
3. Moles (n):
Since the amount of air doubles, the number of moles will also double, assuming the temperature and volume remain constant.
4. Gas constant (R):
The gas constant is a constant value and does not change regardless of the change in the amount of air. Therefore, it stays constant.
5. Temperature (T):
If the amount of air is being added at the same temperature, then the temperature stays constant. If there are changes in temperature, it will affect the other variables, but we are assuming that the temperature remains constant.
To summarize:
Pressure (P): doubles
Volume (V): halves
Moles (n): doubles
Gas constant (R): stays constant
Temperature (T): stays constant
To answer this question, we need to consider the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Given that the life raft initially contains 200 g of air and an additional 200 g of air is added, the total mass of air in the raft is now 400 g.
The number of moles (n) of a gas can be calculated using the molar mass (M) and mass (m) of the gas using the formula n = m/M. Assuming air is composed of mainly nitrogen (N2) and oxygen (O2) with a molar mass of around 28 g/mol and 32 g/mol, respectively, we can calculate the number of moles initially present in the 200 g of air as follows:
n = (200 g)/(28 g/mol) + (200 g)/(32 g/mol)
= 7.14 mol + 6.25 mol
= 13.39 mol (approximately)
Now, when the additional 200 g of air is added, the total number of moles present in the life raft becomes:
n = 13.39 mol + (200 g)/(28 g/mol) + (200 g)/(32 g/mol)
= 13.39 mol + 7.14 mol + 6.25 mol
= 26.78 mol (approximately)
Now, let's consider the changes in pressure, volume, and temperature.
Pressure (P):
The pressure is directly proportional to the number of moles in a gas at a constant temperature and volume. Therefore, since the number of moles has doubled from 13.39 mol to 26.78 mol, the pressure of the air in the life raft will double as well.
Volume (V):
The volume of a fixed amount of gas is inversely proportional to the pressure at a constant temperature. As the pressure doubles, the volume will halve to maintain a constant temperature. Therefore, the volume of air in the life raft will be halved.
Moles (n):
As explained earlier, the number of moles doubles from 13.39 mol to 26.78 mol when an additional 200 g of air is added.
Gas constant (R) and Temperature (T):
The gas constant (R) is a constant value, and the temperature (T) is not specified in the question. Therefore, both the gas constant and the temperature will remain constant in this scenario.
In summary, the changes in the remaining quantities are as follows:
- Pressure (P) will double.
- Volume (V) will halve.
- Moles (n) will double.
- Gas constant (R) will stay constant.
- Temperature (T) will also stay constant.