19. Convert 15 ppm of benzene to mg/m3 at 20 oC and 720 torr
Density of a gas is g/L = P(MW)/RT
(740 torr x 1 atm/760torr)(78.114g/mole)/ (.0821L atm/mole K)(293K) = 3.16g/L
1ppm =1 L Benzene/106 L of air = 1L ben/1000 m of air = 0.001 L ben/m3 = 0.00316 g/m3
x/3.16=15 = 47.4mg/m3 ???
To convert 15 ppm of benzene to mg/m³ at 20°C and 720 torr, we need to use the given density of a gas formula: g/L = P(MW)/RT.
First, let's convert the given pressure from torr to atm:
720 torr x (1 atm / 760 torr) = 0.947 atm
Now, let's calculate the density using the formula. The molar mass of benzene (C₆H₆) is 78.114 g/mol, the universal gas constant (R) is 0.0821 L atm/mol K, and the temperature (T) is 20°C (293K).
Density = (0.947 atm x 78.114 g/mol) / (0.0821 L atm/mol K x 293K) = 3.16 g/L
Next, let's convert the ppm to g/m³.
1 ppm = 1 L benzene / 10^6 L air = 1 L benzene / 1000 m³ air = 0.001 L benzene / m³ air
Now, we can solve for x (the concentration of benzene in mg/m³) using the conversion factor we just derived:
x (mg/m³) / 3.16 (g/m³) = 15 ppm = 15 * 0.001 L benzene / m³ air
Simplifying the equation, we get:
x / 3.16 = 0.015
Solving for x gives:
x = 0.015 * 3.16 = 0.0474 g/m³
Finally, let's convert the concentration to mg/m³:
0.0474 g/m³ = 47.4 mg/m³
Therefore, the concentration of benzene is approximately 47.4 mg/m³ at 20°C and 720 torr.