Question

how many cal need to be removed to condense 50.0 g of steam at 150.0 °c to water at 4.00 °c ? use the conversions given below. first, the steam must first be cooled from 150.0 °c down to 100.0 °c, a change of 1 second, the steam at 100.0 °c must be condensed to water at 2, there is no change in temperature third, the water must be cooled from 100.0 °c to 4.00 °c, a change of 3 the answer is the addition of these three processes (0.497 cal/g°c)(50.0 g)(4) = 5 cal (539 ca/g)(50.0 g) = 6 cal (0.999 cal/g°c))(50.0 g)(7) = 8 cal 9 cal = 10 cal a. 0.504 cal/g °c b. 79.9 cal/g c. 0.999 cal/g °c d. 539 cal/g e. 0.497 cal/g °c f. 150.0 °c g. 100.0 °c h. 50.0 g i. 50.0 °c j. 96.0 °c k. 4.0 °c l. 25.0 °c m. 37.0 °c n. 5.00 g o. 647 p. 33.0 q. 1,243 r. 63.0 s. 4,795 t. 26,950 u. 399.5 v. 184.8 w. 32,988 x. 25.0 °c y. -25.0 °c z. 5.00 aa. 184.8

Explanation:

Step1: Calculate temperature change for cooling steam

The temperature change for cooling steam from \(150.0^{\circ}C\) to \(100.0^{\circ}C\) is \(\Delta T_1=150.0 - 100.0=50.0^{\circ}C\) (I).

Step2: Condensation temperature

Steam condenses to water at \(100.0^{\circ}C\) (G).

Step3: Calculate temperature change for cooling water

The temperature change for cooling water from \(100.0^{\circ}C\) to \(4.00^{\circ}C\) is \(\Delta T_2 = 100.0-4.00 = 96.0^{\circ}C\) (J).

Step4: Calculate heat for cooling steam

Using \(Q_1 = c_1m\Delta T_1\), where \(c_1 = 0.497\ cal/g^{\circ}C\), \(m = 50.0\ g\), \(\Delta T_1=50.0^{\circ}C\). So \(Q_1=(0.497\ cal/g^{\circ}C)(50.0\ g)(50.0^{\circ}C)=1243\ cal\) (Q).

Step5: Calculate heat for condensation

Using \(Q_2 = Lm\), where \(L = 539\ cal/g\), \(m = 50.0\ g\). So \(Q_2=(539\ cal/g)(50.0\ g)=26950\ cal\) (T).

Step6: Calculate heat for cooling water

Using \(Q_3 = c_2m\Delta T_2\), where \(c_2 = 0.999\ cal/g^{\circ}C\), \(m = 50.0\ g\), \(\Delta T_2=96.0^{\circ}C\). So \(Q_3=(0.999\ cal/g^{\circ}C)(50.0\ g)(96.0^{\circ}C)=4795\ cal\) (S).

Step7: Calculate total heat

\(Q = Q_1+Q_2+Q_3=1243 + 26950+4795=32988\ cal\) (W).

Answer:

1. I. \(50.0^{\circ}C\)
2. G. \(100.0^{\circ}C\)
3. J. \(96.0^{\circ}C\)
4. I. \(50.0^{\circ}C\)
5. Q. \(1243\)
6. T. \(26950\)
7. J. \(96.0^{\circ}C\)
8. S. \(4795\)
9. W. \(32988\)
10. W. \(32988\)