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Calculating the molar mass of a gas is a crucial aspect when dealing with gas properties. The molar mass is the measure of the mass of one mole of a substance. For gases, you can find the molar mass using the relationship between mass, moles, and the given mass of the gas. Look at it this way: you already have the mass of the gas given as 7.10 grams, and by using the ideal gas law, you can calculate the number of moles of the gas.
Once you have the number of moles, the formula for molar mass is as follows:

• Molar Mass (M) = \( \frac{\text{mass}}{\text{moles}} \)

This is a ratio where the mass is divided by moles, derived from the ideal gas law calculations. This quick calculation helps in converting the physical attributes of the gas into a more usable form in molecular chemistry.

Pressure conversion is necessary when solving problems related to gases because different pressure units can be used, like torr, atmospheres, pascals, etc. The ideal gas law equation uses atmospheres as the standard unit for pressure.
The given problem has the pressure in torr (741 torr). To convert torr to atmospheres, you use the conversion factor where 1 atm = 760 torr. Thus:

• Pressure in atm = \( \frac{741 \ \text{torr}}{760 \ \text{torr/atm}} \approx 0.975 \ \text{atm} \)

Converting these units ensures that the other constants and units in the ideal gas law equation align correctly, so your calculations are accurate and meaningful.

Temperature needs to be accurately converted when dealing with gas laws, specifically the ideal gas law. The ideal gas law requires Kelvin as the temperature unit because it's an absolute temperature scale, avoiding any negative values which are present in Celsius.
In the problem, the temperature is provided as 44°C, which needs conversion. The conversion formula from Celsius to Kelvin is:

• Temperature in Kelvin = Celsius + 273.15

Therefore:

• Temperature in Kelvin = 44 + 273.15 = 317.15 K

Using Kelvin ensures that the ideal gas law behaves consistently across various conditions, which is critical for understanding the behavior of gases.

To find how many moles of gas are present, which is denoted by \( n \), you rearrange the ideal gas law equation, which is\( PV = nRT \).
This rearrangement becomes \( n = \frac{PV}{RT} \).
For our problem:

• \( P = 0.975 \ \text{atm} \)
• \( V = 5.40 \ \text{L} \)
• \( R = 0.0821 \ \text{L atm/mol K} \)
• \( T = 317.15 \ \text{K} \)

Substituting into the formula:

• \( n = \frac{0.975 \times 5.40}{0.0821 \times 317.15} \)

Perform this calculation to determine the moles of gas. This value is pivotal for further calculations, such as determining the molar mass, by linking physical attributes of the sample to its chemical properties.