Carbon tetrachloride (CCl4), inside a cylinder with A meters height and B meters diameter, is initially at D °C and E kPag. (10 pts) a. What will the pressure be inside the cylinder if the temperature increases to F °C? b. How many grams of hydrogen gas are present inside the cylinder? Note: Assume ideal behavior
Answer (1)
Answer:First, let’s write down everything in SI‐units:Given • Cylinder height A m • Cylinder diameter B m • Initial temperature T₁ = (D + 273.15) K • Initial gauge pressure E kPa(gauge) ⇒ P₁ = [E + 101.325] kPa = [E + 101.325]·10³ Pa We assume the gas in question behaves ideally (whether CCl₄ vapor or H₂—just plug in the appropriate molar mass M)Cylinder volume V = π·(B/2)²·A Molar mass • for CCl₄: M = 12.01 + 4·35.45 = 153.81 g/mol • for H₂: M = 2·1.008 = 2.016 g/mol Universal gas constant R = 8.314 J/(mol·K) –––––––––––––––––––––––––––––––––––––––– (a) New pressure at T₂ = (F + 273.15) K By the ideal‐gas law, at fixed V and n, P₂/P₁ = T₂/T₁ ⇒ P₂ = P₁·(T₂/T₁) If you want gauge pressure again (in kPa gauge), compute P₂(gauge) = [P₂/10³ Pa – 101.325] kPa Putting it all together: P₂(gauge) = { [E + 101.325]·(F + 273.15)/(D + 273.15) – 101.325 } kPa –––––––––––––––––––––––––––––––––––––––– (b) Mass of gas in the cylinder First find the number of moles n from the initial state: n = P₁·V / (R·T₁) = [ (E + 101.325)·10³ Pa · π·(B/2)²·A ] / [ 8.314 J/(mol·K) · (D + 273.15) K ] Then the mass m = n·M. If you want grams, use M in g/mol: m (g) = n (mol) · M (g/mol) Explicitly, for hydrogen (M = 2.016 g/mol): mH₂ = { (E + 101.325)·10³ · π·(B/2)²·A / [8.314·(D + 273.15)] } × 2.016 grams —or for CCl₄ vapor (M = 153.81 g/mol): mCCl₄ = { (E + 101.325)·10³ · π·(B/2)²·A / [8.314·(D + 273.15)] } × 153.81 grams That completes both (a) and (b).
