Question

a 6.00 l tank at 6.08 °c is filled with 7.16 g of dinitrogen monoxide gas and 11.1 g of chlorine pentafluoride gas. you can assume both gases behave as ideal gases under these conditions. calculate the total pressure in the tank. round your answer to the correct number of significant digits. total pressure in tank: atm

Explanation:

Step1: Calculate the number of moles for each gas

• For dinitrogen monoxide (\(N_2O\)):

The molar mass of \(N_2O\) is \(M_{N_2O}=(2\times14.01)+16.00 = 44.02\space g/mol\).
Using the formula \(n=\frac{m}{M}\), where \(m = 7.16\space g\) and \(M = 44.02\space g/mol\), we have \(n_{N_2O}=\frac{7.16}{44.02}\approx0.1627\space mol\).

• For chlorine pentafluoride (\(ClF_5\)):

The molar mass of \(ClF_5\) is \(M_{ClF_5}=35.45+(5\times19.00)=35.45 + 95.00=130.45\space g/mol\).
Using the formula \(n=\frac{m}{M}\), where \(m = 11.1\space g\) and \(M = 130.45\space g/mol\), we have \(n_{ClF_5}=\frac{11.1}{130.45}\approx0.0851\space mol\).

Step2: Calculate the total number of moles

Using the formula \(n_{total}=n_{N_2O}+n_{ClF_5}\), we have \(n_{total}=0.1627 + 0.0851=0.2478\space mol\).

Step3: Convert the temperature to Kelvin

Using the formula \(T = t+273.15\), where \(t = 6.08^{\circ}C\), we have \(T=6.08 + 273.15=279.23\space K\).

Step4: Use the ideal gas law to calculate the total pressure

The ideal gas law is \(PV=nRT\), where \(V = 6.00\space L\), \(n = 0.2478\space mol\), \(R=0.0821\space L\cdot atm/(mol\cdot K)\), and \(T = 279.23\space K\).
Rearranging for \(P\), we get \(P=\frac{nRT}{V}\).
Substituting the values: \(P=\frac{0.2478\times0.0821\times279.23}{6.00}\).
First, calculate \(0.2478\times0.0821\times279.23\approx0.2478\times22.924=5.68\).
Then, \(P=\frac{5.68}{6.00}\approx0.947\space atm\).

Answer:

\(0.947\space atm\)