Argon is a monatomic gas whose atomic mass is 39.9 u. The temperature of eight grams of argon is raised by 95 K under conditions of constant pressure. Assuming that argon behaves as an ideal gas, how much heat is required?
To determine the amount of heat required to raise the temperature of eight grams of argon, we can use the formula:
q = m * c * ΔT
Where:
q = heat (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of argon (in J/g·K)
ΔT = change in temperature (in K)
In this case, the mass of argon (m) is given as eight grams, and the change in temperature (ΔT) is given as 95 K.
To find the specific heat capacity of argon (c), we can use the molar mass of argon and the molar heat capacity of argon at constant pressure (Cp). The molar mass of argon is given as 39.9 g/mol. Cp for argon is approximately 20.8 J/(mol·K).
To calculate the specific heat capacity (c), we can use the following formula:
c = Cp / M
Where:
c = specific heat capacity (in J/g·K)
Cp = molar heat capacity (in J/mol·K)
M = molar mass (in g/mol)
Substituting the given values, we get:
c = 20.8 J/(mol·K) / 39.9 g/mol
Calculating the above expression, we find:
c ≈ 0.522 J/(g·K)
Now, we can substitute the values of m, c, and ΔT into the formula for heat (q) and solve for q:
q = 8 g * 0.522 J/(g·K) * 95 K
Calculating the above expression, we find:
q ≈ 394.56 J
Therefore, approximately 394.56 joules of heat are required to raise the temperature of eight grams of argon by 95 K under constant pressure.
To determine the amount of heat required, you can use the equation:
Q = nCΔT
where:
Q is the amount of heat (in Joules),
n is the number of moles of the gas,
C is the molar heat capacity (in J/(mol·K)),
ΔT is the change in temperature (in Kelvin).
First, let's calculate the number of moles (n) of argon:
n = mass / molar mass
Given that the mass of argon is 8 grams and its molar mass is 39.9 g/mol:
n = 8 g / 39.9 g/mol
n ≈ 0.2005 mol
Next, we need to determine the molar heat capacity of argon (C). For an ideal monatomic gas, the molar heat capacity at constant pressure (Cp) is approximately 5/2 R, where R is the gas constant (8.314 J/(mol·K)):
Cp = 5/2 R
Cp ≈ 5/2 * 8.314 J/(mol·K)
Cp ≈ 20.785 J/(mol·K)
Finally, we can calculate the amount of heat (Q) using the given change in temperature (ΔT = 95 K):
Q = nCpΔT
Q = 0.2005 mol * 20.785 J/(mol·K) * 95 K
Q ≈ 398.8 J
Therefore, approximately 398.8 Joules of heat is required to raise the temperature of 8 grams of argon by 95 K under constant pressure.
Q = mc ΔT
HAve to look up specific heat of Argon