47. complete the following table for an ideal gas. p (atm) v (l) n (mol) t a. 5.00 2.00 155°c b. 0.300 2.00…

47. complete the following table for an ideal gas. p (atm) v (l) n (mol) t a. 5.00 2.00 155°c b. 0.300 2.00 155 k c. 4.47 25.0 2.01 d. 2.25 10.5 75°c

47. complete the following table for an ideal gas. p (atm) v (l) n (mol) t a. 5.00 2.00 155°c b. 0.300 2.00 155 k c. 4.47 25.0 2.01 d. 2.25 10.5 75°c

Answer

  1. Recall the ideal - gas law:
    • The ideal - gas law is given by (PV = nRT), where (P) is the pressure in atmospheres (atm), (V) is the volume in liters (L), (n) is the number of moles, (T) is the temperature in Kelvin (K), and (R=0.08206\ L\cdot atm/(mol\cdot K)).
  2. a. Calculate the volume ((V)):
    • First, convert the temperature to Kelvin. (T=(155 + 273.15)\ K=428.15\ K).
    • From the ideal - gas law (V=\frac{nRT}{P}).
    • Substitute (n = 2.00\ mol), (R = 0.08206\ L\cdot atm/(mol\cdot K)), (T = 428.15\ K), and (P = 5.00\ atm) into the formula.
    • (V=\frac{2.00\ mol\times0.08206\ L\cdot atm/(mol\cdot K)\times428.15\ K}{5.00\ atm})
    • (V=\frac{2.00\times0.08206\times428.15}{5.00}\ L)
    • (V=\frac{70.27}{5.00}\ L = 14.1\ L).
  3. b. Calculate the number of moles ((n)):
    • Use the ideal - gas law (n=\frac{PV}{RT}).
    • Substitute (P = 0.300\ atm), (V = 2.00\ L), (R = 0.08206\ L\cdot atm/(mol\cdot K)), and (T = 155\ K) into the formula.
    • (n=\frac{0.300\ atm\times2.00\ L}{0.08206\ L\cdot atm/(mol\cdot K)\times155\ K})
    • (n=\frac{0.600}{12.72}\ mol=0.0472\ mol).
  4. c. Calculate the temperature ((T)):
    • From the ideal - gas law (T=\frac{PV}{nR}).
    • Substitute (P = 4.47\ atm), (V = 25.0\ L), (n = 2.01\ mol), and (R = 0.08206\ L\cdot atm/(mol\cdot K)) into the formula.
    • (T=\frac{4.47\ atm\times25.0\ L}{2.01\ mol\times0.08206\ L\cdot atm/(mol\cdot K)})
    • (T=\frac{111.75}{0.16494\ mol\cdot K})
    • (T = 677\ K).
  5. d. Calculate the pressure ((P)):
    • First, convert the temperature to Kelvin. (T=(75 + 273.15)\ K = 348.15\ K).
    • From the ideal - gas law (P=\frac{nRT}{V}).
    • Substitute (n = 10.5\ mol), (R = 0.08206\ L\cdot atm/(mol\cdot K)), (T = 348.15\ K), and (V = 2.25\ L) into the formula.
    • (P=\frac{10.5\ mol\times0.08206\ L\cdot atm/(mol\cdot K)\times348.15\ K}{2.25\ L})
    • (P=\frac{10.5\times0.08206\times348.15}{2.25}\ atm)
    • (P=\frac{301.7}{2.25}\ atm = 134\ atm).

The completed table is:

(P) (atm) (V) (L) (n) (mol) (T) (K)
(5.00) (14.1) (2.00) (428.15)
(0.300) (2.00) (0.0472) (155)
(4.47) (25.0) (2.01) (677)
(134) (2.25) (10.5) (348.15)