A new element E forms a conpound EClx(x is subscript) which contains 1.455 gram Cl per gram E. The specific heat of E was found 0.05 calorie per gram. If equivalent weight of element is 24. Find x

To solve the problem of determining the value of x in the compound EClx, we need to analyze the information given about the element E and its relationship with chlorine (Cl). Let's break it down step by step.

Understanding the Relationship Between E and Cl

We know that the compound EClx contains a specific ratio of chlorine to the element E. The problem states that there are 1.455 grams of Cl per gram of E. This means we can express the mass of chlorine in terms of the mass of E:

• Mass of Cl = 1.455 grams
• Mass of E = 1 gram

Calculating the Molar Mass of Chlorine

The molar mass of chlorine (Cl) is approximately 35.5 grams per mole. To find out how many moles of Cl correspond to 1.455 grams, we can use the formula:

Number of moles of Cl = Mass of Cl / Molar mass of Cl

Substituting the values:

Number of moles of Cl = 1.455 g / 35.5 g/mol ≈ 0.0410 moles

Finding the Moles of Element E

Since the compound is EClx, we know that for every 1 mole of E, there are x moles of Cl. Therefore, we can express this relationship as:

Number of moles of E = Number of moles of Cl / x

Using Equivalent Weight to Find Moles of E

The equivalent weight of an element is defined as the mass of the element that combines with or displaces 1 mole of hydrogen or 8 grams of oxygen. In this case, the equivalent weight of E is given as 24 grams. The relationship between equivalent weight and moles is:

Moles of E = Mass of E / Equivalent weight of E

Since we have 1 gram of E, we can calculate the moles of E:

Moles of E = 1 g / 24 g/equiv ≈ 0.04167 moles

Setting Up the Equation

Now we can set the two expressions for moles of E equal to each other:

0.04167 = 0.0410 / x

Solving for x

To find x, we can rearrange the equation:

x = 0.0410 / 0.04167

x ≈ 0.983

Since x must be a whole number in the context of chemical formulas, we round it to the nearest whole number, which gives us:

x = 1

Final Thoughts

Thus, the value of x in the compound EClx is 1, indicating that the compound is likely ECl. This analysis shows how we can use the relationships between mass, moles, and equivalent weight to derive important information about chemical compounds. If you have any further questions or need clarification on any of the steps, feel free to ask!