Question

Tim has a bottle of Oxygen being stored in his garage. When he checks the pressure on the tank he finds that it is under 2900 mmHg. He finds the density of Oxygen is 1.43 g/L. What is the temperature in Celsius of the room

Answer 1

769.47°C

Step-by-step explanation:

Step 1:

Data obtained from the question:

Pressure (P) = 2900 mmHg

Density (D) = 1.43 g/L

Temperature (T) =?

Step 2:

Conversion of 2900 mmHg to atm. This is illustrated below:

760mmHg = 1atm

Therefore, 2900 mmHg = 2900/760 = 3.82 atm

Step 3:

Finding an expression which relates density, pressure and temperature together. This is illustrated below:

From ideal gas equation,

PV = nRT (1)

Divide both side by P

V = nRT/P (2)

Recall:

Number of mole(n) = mass(m)/Molar Mass(M)

n = m/M

Substituting the value of n into equation 2, we obtained:

V = nRT/P

V = mRT/MP

Divide both side by m

V/m = RT/MP

Invert the equation

m/V = MP/RT (3)

But Density(D) = Mass(m)/volume(V)

D = m/V

Replace m/V with D in equation 3.

m/V = MP/RT

D = MP/RT

M (molar mass of oxygen) = 16x2 = 32g/mol

R (gas constant) = 0.082atm.L/Kmol

Step 4:

Determination of the temperature. This is illustrated below:

M = 32g/mol

P = 3.82 atm

R = 0.082atm.L/Kmol

D = 1.43g/L

T =?

D = MP/RT

1.43 = (32 x 3.82)/ 0.082 x T

Cross multiply to express in linear form

1.43 x 0.082 x T = 32 x 3.82

Divide both side by 1.43 x 0.082

T = (32 x 3.82) / (1.43 x 0.082)

T = 1042.47K

Step 5:

Conversion of 1042.47K to celsius temperature. This is illustrated below:

°C = K - 273

°C = 1042.47K - 273

°C = 769.47°C