What is the molecular mass of a gas that has a density of 0.897 g/L if it exerts a pressure of 1.35 ATM and is that a temperature of 43.5°C?
p*molar mass = density*RT
Remember T must be in kelvin.
assume 100Liters, mass then is 89.7 grams
PV=nRT
so you have P, v(100lites), n=mass/molmass and you know mass, Look up R for your units, and you know temperature
To find the molecular mass of a gas, you 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, and T is the temperature.
Step 1: Convert the temperature to Kelvin.
To convert from Celsius to Kelvin, add 273.15 to the temperature given. In this case, 43.5°C + 273.15 = 316.65 K.
Step 2: Convert the pressure from ATM to mmHg.
Since the gas constant (R) is commonly expressed in terms of mmHg, we need to convert the pressure from ATM to mmHg. 1 ATM is equal to 760 mmHg. So, 1.35 ATM * 760 mmHg/1 ATM = 1026 mmHg.
Now we have:
Pressure (P) = 1026 mmHg,
Volume (V) = unknown,
Number of moles (n) = unknown,
Gas constant (R) = 0.0821 L·atm/(mol·K),
Temperature (T) = 316.65 K.
Step 3: Rearrange the Ideal Gas Law equation to solve for the number of moles (n).
Since we are trying to find the molecular mass, which is directly proportional to the number of moles, we rearrange the equation to solve for n: n = (PV) / (RT).
Step 4: Calculate the number of moles (n).
Plug in the values into the rearranged equation: n = (1026 mmHg * V) / (0.0821 L·atm/(mol·K) * 316.65 K).
Step 5: Solve for the volume (V).
Rearrange the equation to solve for V: V = (n * R * T) / P.
Step 6: Calculate the volume (V).
Substitute the known values into the equation: V = (n * 0.0821 L·atm/(mol·K) * 316.65 K) / 1026 mmHg.
Step 7: Convert density to moles per liter.
Given that density (d) = 0.897 g/L, we can use this value to convert to moles per liter.
Step 8: Calculate the number of moles (n).
Using the formula: n = d * V, where d is density and V is volume.
Step 9: Calculate the molecular mass (m).
The molecular mass (m) can be calculated using the formula: m = mass / moles.
Substitute the known values into the equation: m = mass / n.
Hence, to find the molecular mass, you need to calculate the mass and the number of moles as explained above.