## Gases Exam4 and Problem Solutions

**Gases Exam4 and Problem Solutions**

**1. **Find density of C_{4}H_{8} under 273 ^{0}C temperature and 2 atm pressure. (H=1, C=12)

**Solution:**

T=273 + 273 = 546 ^{0}K

P=2atm and Molar mass of C_{4}H_{8}=4.(12) + 8(1)=56g/mol

We use ideal gas law to find density of gas;

P.M_{C4H8}=d.R.T

2.56=d.0,082.546

d=2,5g/L

**2.** If sum of pressures of 1,6g He and 0,8g CH_{4} gases is 0,9atm, find partial pressures of He and CH_{4}.(He=4, C=12, H=1)

**Solution:**

Moles of gases;

n_{He}=1,6/4=0,4mol

n_{CH4}=0,8/16=0,05mol

n_{total}=0,4 + 0,05=0,45mol

Partial pressures of gases are found by formula;** P _{x}=(n_{x}/n_{total}).P_{total}**

P_{He}=0,4/0,45,0,0=0,8atm

P_{CH4}=0,05/0,45.0,4=0,1atm

**3.** There are He gas in given container. Which one of the following statements are true for this container under constant temperature?

**I.** If we add CH_{4} gas into container, partial pressure of He increases.

**II.** If we add O_{2}(g) into container, density of the gases in container increases.

**III.** If we add Ar gas into container, average kinetic energy stays constant.

**Solution: **

**I. **Adding CH_{4} into container increases total number of moles but mole of He does not change, so its partial pressure stays constant. I is false.

**II.** If we add O_{2}(g) into container, total mass of gases increases and since volume is constant, density of gases increases. II is true.

**III.** All gases have same average kinetic energy under same temperature. III is true.

**4.** Which ones of the following statements are true for CH_{4} and He given in picture below;

**I.** Pressures of CH_{4} and He are equal.

**II.** Number of collisions to unit surface in unit time are equal to each other.

**III.** Their densities are equal.

**Solution:**

**I.** Since CH_{4} and He has equal volume, temperature and mole their pressures are also equal. I is true.

**II.** Number of collisions in unit time id directly proportional to speed of gases.

Speed of He is larger than speed of CH_{4}, so number of collisions of He is larger than number of collisions of CH_{4}.II is false.

**III. **Since molar masses of CH_{4} and He are different, their densities are also different. III is false.

**5.** There are some ideal gas in a closed container having constant volume. Which ones of the graphs given below are true for this gas? (P:Pressure, T:Temperature, d:Density)

**Solution:**

**I.** Since number of moles and volume of gas are constant, increasing temperature increases pressure. I is true.

**II. **P.V is directly proportional to temperature and number of moles. Since mole of gas is constant and T increases; P.V also increases. II is true.

**III. **Since number of moles, volume and mass of gas are constant; density stays constant. III is true.

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