Question

what is the molar mass of a gas if 0.0494 g of the gas occupies a volume of 0.100 l at a temperature of 26°c and a pressure of 307 torr?
2.61 g/mol
30.0 g/mol
0.395 g/mol
0.00343 g/mol
the density of a certain gaseous fluoride of phosphorus is 3.93 g/l at stp. calculate the molar mass of the compound.
g/mol
which of the following is the molecular formula of the gas described in the previous question?
p₂f₃
pf₃
p₂f
pf₂
p₂f₂

Explanation:

First Question

Step1: Convert units

• Convert pressure: \(P = 307\ torr\times\frac{1\ atm}{760\ torr}\approx0.404\ atm\)
• Convert temperature: \(T=(26 + 273.15)\ K=299.15\ K\)
• Use the ideal gas law \(PV=nRT\), and \(n=\frac{m}{M}\), so \(PV=\frac{m}{M}RT\), then \(M=\frac{mRT}{PV}\)
• \(R = 0.0821\ L\cdot atm/(mol\cdot K)\), \(m = 0.0494\ g\), \(V=0.100\ L\)

Step2: Calculate molar mass

$$
LATEXBLOCK0
$$

Step1: Use the formula for density at STP

At STP (\(T = 273\ K\), \(P=1\ atm\)), the ideal gas law \(PV=nRT\) can be rewritten as \(P=\frac{m}{MV}RT\) (since \(n=\frac{m}{M}\)), and density \(
ho=\frac{m}{V}\). So \(M=
ho\times\frac{RT}{P}\)

• \(

ho = 3.93\ g/L\), \(R = 0.0821\ L\cdot atm/(mol\cdot K)\), \(T = 273\ K\), \(P = 1\ atm\)

Step2: Calculate molar mass

$$
LATEXBLOCK0
$$

Step1: Calculate molar masses of options

• For \(P_2F_3\): \(M=(2\times30.97+3\times19.00)\ g/mol=(61.94 + 57.00)\ g/mol=118.94\ g/mol\)
• For \(PF_3\): \(M=(30.97+3\times19.00)\ g/mol=(30.97+57.00)\ g/mol = 87.97\approx88.0\ g/mol\)
• For \(P_2F\): \(M=(2\times30.97+19.00)\ g/mol=(61.94+19.00)\ g/mol=80.94\ g/mol\)
• For \(PF_2\): \(M=(30.97+2\times19.00)\ g/mol=(30.97 + 38.00)\ g/mol=68.97\ g/mol\)
• For \(P_2F_2\): \(M=(2\times30.97+2\times19.00)\ g/mol=(61.94+38.00)\ g/mol = 99.94\ g/mol\)

Answer:

\(30.0\ g/mol\)

Second Question