A quantity of gas weighing 7.10g at 741 torr and 44 degrees C occupies a volume of 5.40 L. What is its molar mass?

PV=nRT

solve for moles, n. then, molmass=mass/moles

To find the molar mass of the gas, we can use the ideal gas law:

PV = nRT

Where:
P = pressure = 741 torr
V = volume = 5.40 L
n = number of moles of gas
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin

First, let's convert the temperature from degrees Celsius to Kelvin using the equation:

T(K) = T(°C) + 273.15

T(K) = 44°C + 273.15 = 317.15 K

Now, we can rearrange the ideal gas law and solve for the number of moles (n) of gas:

n = PV / (RT)

n = (741 torr * 5.40 L) / (0.0821 L·atm/(mol·K) * 317.15 K)

n ≈ 0.18 mol

Next, we can calculate the molar mass (M) of the gas using the equation:

M = mass / n

M = 7.10 g / 0.18 mol

M ≈ 39.44 g/mol

Therefore, the molar mass of the gas is approximately 39.44 g/mol.

To find the molar mass of a gas, we need to use the ideal gas law equation, which is:

PV = nRT

Where:
P is the pressure of the gas (in torr)
V is the volume of the gas (in liters)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/(mol·K) or 62.36 L·torr/(mol·K))
T is the temperature of the gas (in Kelvin)

First, we need to convert the given temperature from Celsius to Kelvin. We can do this by adding 273.15 to the Celsius temperature:

44°C + 273.15 = 317.15 K

Now, let's substitute the given values into the ideal gas law equation:

(741 torr)(5.40 L) = n(0.0821 L·atm/(mol·K))(317.15 K)

Simplifying the equation, we get:

4004.4 = n(26.08)

Next, solve for the number of moles (n):

n = 4004.4 / 26.08
n ≈ 153.43 moles

Lastly, calculate the molar mass (M) by dividing the mass of the gas (in grams) by the number of moles:

M = mass of gas / n

Given that the mass of the gas is 7.10g, we can substitute the values:

M = 7.10 g / 153.43 mol
M ≈ 0.046 g/mol

Therefore, the molar mass of the gas is approximately 0.046 g/mol.