Questions: An ideal gas originally at 0.85 atm and 66°C was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45°C, respectively. What was its initial volume? Calculate its volume (in liters) of 88.4 g of CO2 at STP. A gas at 772 mmHg and 35.0°C occupies a volume of 6.85 L. Calculate its volume at STP. Dry ice is solid carbon dioxide. A 0.050-g sample of dry ice is placed in an evacuated 4.6-L vessel at 30°C. Calculate the pressure inside the vessel after all the dry ice has been converted to CO2 gas. At STP, 0.280 L of a gas weighs 0.400 g. Calculate the molar mass of the gas. At 741 torr and 44°C, 7.10 g of a gas occupy a volume of 5.40 L. What is the molar mass of the gas? Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and 1.0 x 10^-3 atm, respectively. How many ozone molecules are present in 1.0 L of air under these conditions? Assuming that air contains 78% N2, 21% O2, and 1% Ar, all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP? A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0°C. a. Calculate the density of the gas in grams per liter b. What is the molar mass of the gas? Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and 46°C.

An ideal gas originally at 0.85 atm and 66°C was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45°C, respectively. What was its initial volume? Calculate its volume (in liters) of 88.4 g of CO2 at STP. A gas at 772 mmHg and 35.0°C occupies a volume of 6.85 L. Calculate its volume at STP. Dry ice is solid carbon dioxide. A 0.050-g sample of dry ice is placed in an evacuated 4.6-L vessel at 30°C. Calculate the pressure inside the vessel after all the dry ice has been converted to CO2 gas. At STP, 0.280 L of a gas weighs 0.400 g. Calculate the molar mass of the gas. At 741 torr and 44°C, 7.10 g of a gas occupy a volume of 5.40 L. What is the molar mass of the gas? Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and 1.0 x 10^-3 atm, respectively. How many ozone molecules are present in 1.0 L of air under these conditions? Assuming that air contains 78% N2, 21% O2, and 1% Ar, all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP? A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0°C. a. Calculate the density of the gas in grams per liter b. What is the molar mass of the gas? Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and 46°C.
Transcript text: 5.39 An ideal gas originally at 0.85 atm and $66^{\circ} \mathrm{C}$ was allowed to expand until its final volume, pressure, and temperature were $94 \mathrm{~mL}, 0.60 \mathrm{~atm}$, and $45^{\circ} \mathrm{C}$, respectively. What was its initial volume? 5.40* Calculate its volume (in liters) of 88.4 g of $\mathrm{CO}_{2}$ at STP. 5.41 A gas at 772 mmHg and $35.0^{\circ} \mathrm{C}$ occupies a volume of 6.85 L . Calculate its volume at STP. 5.42* Dry ice is solid carbon dioxide. A 0.050-g sample of dry ice is placed in an evacuated 4.6-L vessel at $30^{\circ} \mathrm{C}$. Calculate the pressure inside the vessel after all the dry ice has been converted to $\mathrm{CO}_{2}$ gas. 5.43 At STP, 0.280 L of a gas weighs 0.400 g . Calculate the molar mass of the gas. $5.44 *$ At 741 torr and $44^{\circ} \mathrm{C}, 7.10 \mathrm{~g}$ of a gas occupy a volume of 5.40 L . What is the molar mass of the gas? 5.45 Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and $1.0 \times 10^{-3} \mathrm{~atm}$, respectively. How many ozone molecules are present in 1.0 L of air under these conditions? $5.46 *$ Assuming that air contains $78 \% \mathrm{~N}_{2}, 21 \% \mathrm{O}_{2}$, and $1 \% \mathrm{Ar}$, all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP? 5.47 A $2.10-\mathrm{L}$ vessel contains 4.65 g of a gas at 1.00 atm and $27.0^{\circ} \mathrm{C}$. a. Calculate the density of the gas in grams per liter b. What is the molar mass of the gas? $5.48 *$ Calculate the density of hydrogen bromide $(\mathrm{HBr})$ gas in grams per liter at 733 mmHg and $46^{\circ} \mathrm{C}$.
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Solution

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Solution Steps

Step 1: Identify the given values and the unknown

For question 5.39, we are given:

  • Initial pressure, \( P_1 = 0.85 \) atm
  • Initial temperature, \( T_1 = 66^{\circ} \mathrm{C} = 66 + 273.15 = 339.15 \) K
  • Final volume, \( V_2 = 94 \) mL
  • Final pressure, \( P_2 = 0.60 \) atm
  • Final temperature, \( T_2 = 45^{\circ} \mathrm{C} = 45 + 273.15 = 318.15 \) K

We need to find the initial volume, \( V_1 \).

Step 2: Use the combined gas law

The combined gas law is given by: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

Step 3: Rearrange the equation to solve for \( V_1 \)

\[ V_1 = \frac{P_2 V_2 T_1}{P_1 T_2} \]

Step 4: Substitute the known values into the equation

\[ V_1 = \frac{(0.60 \, \text{atm}) (94 \, \text{mL}) (339.15 \, \text{K})}{(0.85 \, \text{atm}) (318.15 \, \text{K})} \]

Step 5: Calculate the initial volume

\[ V_1 = \frac{(0.60 \times 94 \times 339.15)}{(0.85 \times 318.15)} \] \[ V_1 = \frac{19118.26}{270.4275} \approx 70.70 \, \text{mL} \]

Final Answer

\[ \boxed{V_1 = 70.70 \, \text{mL}} \]

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