Under which temperature and pressure conditions will the volume of a gas be greatest?
a
T = 700K and P = 2 atm
b
T = 200K and P = 4 atm
c
T = 700K and P = 4 atm
d
T = 200 K and P = 2 atm
c
T = 700K and P = 4 atm
To determine the conditions under which the volume of a gas will be greatest, we need to consider the relationship between temperature, pressure, and volume described by the ideal gas law.
The ideal gas law is given by the equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we want to find the conditions that will maximize the volume (V) for a given value of the pressure (P).
According to the ideal gas law, if the pressure (P) is kept constant, the volume (V) of a gas is directly proportional to the temperature (T). This means that as the temperature increases, the volume also increases, and vice versa.
From the given options, the condition that will result in the greatest volume of gas is when the temperature (T) is highest. Therefore, the answer is option a) T = 700K and P = 2 atm.
To determine under which temperature and pressure conditions the volume of a gas will be greatest, we need to apply the ideal gas law, which states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Rearranging this equation, we get:
V = (nRT)/P
Thus, the volume of a gas is directly proportional to the amount of substance (moles), temperature, and the gas constant, and inversely proportional to the pressure.
Now, let's analyze the options:
a) T = 700K and P = 2 atm
b) T = 200K and P = 4 atm
c) T = 700K and P = 4 atm
d) T = 200 K and P = 2 atm
To determine the condition that results in the greatest volume, we need to look for the combination of high temperature, low pressure, or both.
Option a) has a high temperature, but a moderate pressure.
Option b) has a low temperature and a high pressure.
Option c) has a high temperature and a high pressure.
Option d) has a low temperature and a moderate pressure.
Based on the ideal gas law, the combination that will yield the greatest volume is the one with a high temperature and a low pressure. Therefore, the answer is option a) T = 700K and P = 2 atm.